Show that the points form the vertices of the indicated polygon.
Isosceles triangle: (7, 1), (5, 4), (2, 6)

A)Distances between the points: $\sqrt { 19 } , \sqrt { 13 } , \sqrt { 50 }$
B)Distances between the points: $\sqrt { 13 } , \sqrt { 13 } , \sqrt { 50 }$
C)Distances between the points: $\sqrt { 43 } , \sqrt { 13 } , \sqrt { 50 }$
D)Distances between the points: $\sqrt { 26 } , \sqrt { 13 } , \sqrt { 50 }$
E)Distances between the points: $\sqrt { 37 } , \sqrt { 13 } , \sqrt { 50 }$

Question

Show that the points form the vertices of the indicated polygon.  
Isosceles triangle: (7, 1), (5, 4), (2, 6)
 
A)Distances between the points: $\sqrt { 19 } , \sqrt { 13 } , \sqrt { 50 }$
B)Distances between the points: $\sqrt { 13 } , \sqrt { 13 } , \sqrt { 50 }$
C)Distances between the points: $\sqrt { 43 } , \sqrt { 13 } , \sqrt { 50 }$
D)Distances between the points: $\sqrt { 26 } , \sqrt { 13 } , \sqrt { 50 }$
E)Distances between the points: $\sqrt { 37 } , \sqrt { 13 } , \sqrt { 50 }$

Quizplus · Accepted Answer

To determine if the points form an isosceles triangle, we calculate the distances between each pair of points using the distance formula $d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$.1. Distance between (7, 1) and (5, 4):$$d = \sqrt{(5 - 7)^2 + (4 - 1)^2} = \sqrt{(-2)^2 + 3^2} = \sqrt{4 + 9} = \sqrt{13}$$2. Distance between (5, 4) and (2, 6):$$d = \sqrt{(2 - 5)^2 + (6 - 4)^2} = \sqrt{(-3)^2 + 2^2} = \sqrt{9 + 4} = \sqrt{13}$$3. Distance between (7, 1) and (2, 6):$$d = \sqrt{(2 - 7)^2 + (6 - 1)^2} = \sqrt{(-5)^2 + 5^2} = \sqrt{25 + 25} = \sqrt{50}$$These distances show that two sides of the triangle are equal ($\sqrt{13}$), indicating it is an isosceles triangle, which matches choice B.

Show That the Points Form the Vertices of the Indicated 19,13,50\sqrt { 19 } , \sqrt { 13 } , \sqrt { 50 }19​,13​,50​

Show That the Points Form the Vertices of the Indicated $\sqrt { 19 } , \sqrt { 13 } , \sqrt { 50 }$