Question 1

Find the distance d(  between the points 
-
A)5
B)10
C) 
D)25

Accepted Answer

The answer of Find the distance d(  between the...

Question 2

Solve the problem.
-A motorcycle and a car leave an intersection at the same time. The motorcycle heads north at an averagespeed of 20 miles per hour, while the car heads east at an average speed of 48 miles per hour. Find anexpression for their distance apart in miles at the end of t hours.
A)52t miles
B)  miles
C)  miles
D)  miles

Accepted Answer

The answer of Solve the problem.
-A motorcycle and a car...

Question 3

Find the distance d(  between the points 
-
A) 
B) 
C)12
D)6

Accepted Answer

The answer of Find the distance d(  between the...

Question 4

Solve the problem.
-Find all values of k so that the given points are  units apart.(-5, 5), (k, 0)
A)-3, -7
B)-7
C)3, 7
D)7

Accepted Answer

The answer of Solve the problem.
-Find all values of k...

Question 5

Decide whether or not the points are the vertices of a right triangle.
-(-7, -1), (1, -1), (1, 4)
A)Yes
B)No

Accepted Answer

The points form a right triangle because the sides formed by these points are perpendicular to each other, which is a characteristic of a right triangle. Specifically, the line segments connecting (-7, -1) to (1, -1) and (1, -1) to (1, 4) are perpendicular, as one is horizontal and the other is vertical.

Question 6

Find the distance d(  between the points 
-
A) 
B) 
C)12
D)6

Accepted Answer

The answer of Find the distance d(  between the...

Question 7

Solve the problem.
-A middle schoolʹs baseball playing field is a square, 55 feet on a side. How far is it directly from homeplate to second base (the diagonal of the square)? If necessary, round to the nearest foot.
A)78 feet
B)79 feet
C)77 feet
D)85 feet

Accepted Answer

The diagonal of a square can be found using the formula: diagonal = side * √2. For a square with a side of 55 feet, the diagonal is 55 * √2 ≈ 77.78 feet, which rounds to 78 feet.

Question 8

Find the distance d(  between the points 
- Round to three decimal places, if necessary.
A)2
B)14
C)6.325
D)2.1

Accepted Answer

The answer of Find the distance d(  between the...

Question 9

Find the distance d(  between the points 
-
A) 
B) 
C)90
D)1

Accepted Answer

The answer of Find the distance d(  between the...

Question 10

Find the distance d(  between the points 
-
A)9
B)3
C)10
D)8

Accepted Answer

The answer of Find the distance d(  between the...

Question 11

Find the distance d(  between the points 
-
A)5
B)25
C)6
D)10

Accepted Answer

The answer of Find the distance d(  between the...

Question 12

Find the distance d(  between the points 
-
A) 
B)109
C)7
D)

Accepted Answer

The answer of Find the distance d(  between the...

Question 13

Decide whether or not the points are the vertices of a right triangle.
-(-6, -6), (0, -4), (6, -11)
A)Yes
B)No

Accepted Answer

To determine if a triangle is a right triangle, we need to check if the square of the longest side is equal to the sum of the squares of the other two sides. Using the distance formula, we find that the distances between the points are:
√(36+4) ≈ 6.08   for (-6, -6) to (0, -4)
√(36+49) ≈ 9.22   for (-6, -6) to (6, -11)
√(81+49) = 10      for (0, -4) to (6, -11)
The longest side is between (-6, -6) and (6, -11), so we need to check if the square of 9.22 is equal to the sum of the squares of 6.08 and 10, but it is not. Therefore, the points do not form a right triangle. If we calculate the distance between each pair of points, we get: 
- Distance between (-6,-6) and (0,-4) is approximately 3.6. 
- Distance between (-6,-6) and (6,-11) is approximately 7.8.
- Distance between (0,-4) and (6,-11) is approximately 8.2. 
These distances do not satisfy the Pythagorean theorem, which states that for a right triangle, the square of the length of the hypotenuse (longest side) is equal to the sum of the squares of the lengths of the other two sides. Therefore, these points are not the vertices of a right triangle.

Question 14

Decide whether or not the points are the vertices of a right triangle.
-(3, 0), (9, 2), (8, -3)
A)Yes
B)No

Accepted Answer

We need to check whether any of the three sides has a length equal to the square root of the sum of the squares of the other two. However, none of the three sides satisfy this condition, so the points do not form a right triangle. To determine if these points form a right triangle, we need to calculate the lengths of each side and check if the Pythagorean theorem holds true. Calculating the distance between (3, 0) and (9, 2), we get √((9-3)^2 + (2-0)^2) = √52. Calculating the distance between (3, 0) and (8, -3), we get √((8-3)^2 + (-3-0)^2) = √34. Calculating the distance between (9, 2) and (8, -3), we get √((8-9)^2 + (-3-2)^2) = √10. Now, applying the Pythagorean theorem to see if these sides form a right triangle: √52^2 = √34^2 + √10^2, which simplifies to 52 = 44 + 10. This is not true, so the points do not form a right triangle.

Question 15

Solve the problem.
-Find the area of the right triangle ABC with A = (-2, 7), B = (7, -1), C = (3, 9).
A)29 square units
B)58 square units
C)  square units
D)  square units

Accepted Answer

The answer of Solve the problem.
-Find the area of the...

Question 16

Decide whether or not the points are the vertices of a right triangle.
-(3, 2), (5, 6), (7, 5)
A)Yes
B)No

Accepted Answer

To determine if the points form a right triangle, we can use the distance formula to calculate the lengths of the sides and then apply the Pythagorean theorem. The distance between two points $(x_1, y_1)$ and $(x_2, y_2)$ is given by $\sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}$.1. Distance between (3, 2) and (5, 6): $\sqrt{(5-3)^2 + (6-2)^2} = \sqrt{4 + 16} = \sqrt{20}$2. Distance between (5, 6) and (7, 5): $\sqrt{(7-5)^2 + (5-6)^2} = \sqrt{4 + 1} = \sqrt{5}$3. Distance between (3, 2) and (7, 5): $\sqrt{(7-3)^2 + (5-2)^2} = \sqrt{16 + 9} = \sqrt{25}$The lengths of the sides are $\sqrt{20}$, $\sqrt{5}$, and $\sqrt{25}$. According to the Pythagorean theorem, if these lengths form a right triangle, then the sum of the squares of the two shorter sides should equal the square of the longest side. Checking this, we have $\sqrt{20}^2 + \sqrt{5}^2 = 20 + 5 = 25$, which equals $\sqrt{25}^2$. Therefore, the points do form a right triangle.

Question 17

Find the distance d(  between the points 
-
A) 
B) 
C)12
D)6

Accepted Answer

The answer of Find the distance d(  between the...

Question 18

Solve the problem.
-A rectangular city park has a jogging loop that goes along a length, width, and diagonal of the park. To thenearest yard, find the length of the jogging loop, if the length of the park is 125 yards and its width is 75yards.
A)346 yards
B)146 yards
C)345 yards
D)145 yards

Accepted Answer

The diagonal of a rectangle is the hypotenuse of a right triangle with legs equal to the length and width of the rectangle. Using the Pythagorean Theorem, we have:diagonal^2 = length^2 + width^2diagonal^2 = 125^2 + 75^2diagonal^2 = 22,500diagonal = sqrt(22,500)diagonal = 150 yardsThe jogging loop is the sum of the length, width, and diagonal of the park:jogging loop = length + width + diagonaljogging loop = 125 yards + 75 yards + 150 yardsjogging loop = 346 yards

Question 19

Solve the problem.
-Find all the points having an x-coordinate of 9 whose distance from the point (3, -2)is 10.
A)(9, 6), (9, -10)
B)(9, 2), (9, -4)
C)(9, -12), (9, 8)
D)(9, 13), (9, -7)

Accepted Answer

The distance between two points $(x_1, y_1)$ and $(x_2, y_2)$ is given by the formula $\sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}$. Here, we're given one point $(3, -2)$ and a distance of 10, with the x-coordinate of the other point being 9. Plugging these into the distance formula, we get $\sqrt{(9-3)^2 + (y-(-2))^2} = 10$. Simplifying, $\sqrt{36 + (y+2)^2} = 10$. Squaring both sides gives $36 + (y+2)^2 = 100$, leading to $(y+2)^2 = 64$. Solving for $y$, we find $y+2 = 8$ or $y+2 = -8$, giving $y = 6$ or $y = -10$. Therefore, the points are $(9, 6)$ and $(9, -10)$.

Question 20

Find the distance d(  between the points 
-
A) 
B) 
C)45
D)3

Accepted Answer

The answer of Find the distance d(  between the...

Quiz 2: Graphs

Find the distance d( between the points -

Solve the problem. -A motorcycle and a car leave an intersection at the same time. The motorcycle heads north at an averagespeed of 20 miles per hour, while the car heads east at an average speed of 48 miles per hour. Find anexpression for their distance apart in miles at the end of t hours.

Find the distance d( between the points -

Solve the problem. -Find all values of k so that the given points are units apart.(-5, 5) , (k, 0)

Decide whether or not the points are the vertices of a right triangle. -(-7, -1) , (1, -1) , (1, 4)

Find the distance d( between the points -

Solve the problem. -A middle schoolʹs baseball playing field is a square, 55 feet on a side. How far is it directly from homeplate to second base (the diagonal of the square) ? If necessary, round to the nearest foot.

Find the distance d( between the points - Round to three decimal places, if necessary.

Find the distance d( between the points -

Find the distance d( between the points -

Find the distance d( between the points -

Find the distance d( between the points -

Decide whether or not the points are the vertices of a right triangle. -(-6, -6) , (0, -4) , (6, -11)

Decide whether or not the points are the vertices of a right triangle. -(3, 0) , (9, 2) , (8, -3)

Solve the problem. -Find the area of the right triangle ABC with A = (-2, 7) , B = (7, -1) , C = (3, 9) .

Decide whether or not the points are the vertices of a right triangle. -(3, 2) , (5, 6) , (7, 5)

Find the distance d( between the points -

Solve the problem. -A rectangular city park has a jogging loop that goes along a length, width, and diagonal of the park. To thenearest yard, find the length of the jogging loop, if the length of the park is 125 yards and its width is 75yards.

Solve the problem. -Find all the points having an x-coordinate of 9 whose distance from the point (3, -2) is 10.

Find the distance d( between the points -