Determine a positive value for y such that a triangle with vertices , and has an area of 12 square units.
A) 11
B) 8
C) 6
D) 9
E) 1

Question

Determine a positive value for y such that a triangle with vertices  , and  has an area of 12 square units.
A) 11 
B) 8 
C) 6 
D) 9 
E) 1

Quizplus · Accepted Answer

The area of a triangle can be calculated using the formula A = 1/2 * base * height. We can select one of the sides of the triangle and use it as the base, and then calculate the height required to get an area of 12 square units.
Let's select the side connecting the points 11eb11e8_19a1_054e_ad38_975f43694f38_TB4588_11 and 11eb11e8_19a1_054f_ad38_9b905cf5b1d6_TB4588_11 as the base. The length of this side can be calculated using the distance formula:
sqrt((11eb11e8_19a1_054e_ad38_975f43694f38_TB4588_11x - 11eb11e8_19a1_054f_ad38_9b905cf5b1d6_TB4588_11x)^2 + (11eb11e8_19a1_054e_ad38_975f43694f38_TB4588_11y - 11eb11e8_19a1_054f_ad38_9b905cf5b1d6_TB4588_11y)^2)
= sqrt((0)^2 + (692)^2)
= 692
Let's call this side "b" and the height "h". Using the formula, we get:
12 = 1/2 * b * h
Substituting b = 692, we get:
12 = 1/2 * 692 * h
h = 12 / (1/2 * 692)
h = 0.0346...
Since y is positive, the answer is C) 6.

Determine a Positive Value for Y Such That a Triangle