Show that the points form the vertices of the indicated polygon.
Isosceles triangle: (7, -6), (9, 8), (-5, 6)

A)Distances between the points: $\sqrt { 37 } , \sqrt { 200 } , \sqrt { 288 }$
B)Distances between the points: $\sqrt { 200 } , \sqrt { 200 } , \sqrt { 288 }$
C)Distances between the points: $\sqrt { 26 } , \sqrt { 200 } , \sqrt { 288 }$
D)Distances between the points: $\sqrt { 43 } , \sqrt { 200 } , \sqrt { 288 }$
E)Distances between the points: $\sqrt { 19 } , \sqrt { 200 } , \sqrt { 288 }$

Question

Show that the points form the vertices of the indicated polygon.  
Isosceles triangle: (7, -6), (9, 8), (-5, 6)
 
A)Distances between the points: $\sqrt { 37 } , \sqrt { 200 } , \sqrt { 288 }$
B)Distances between the points: $\sqrt { 200 } , \sqrt { 200 } , \sqrt { 288 }$
C)Distances between the points: $\sqrt { 26 } , \sqrt { 200 } , \sqrt { 288 }$
D)Distances between the points: $\sqrt { 43 } , \sqrt { 200 } , \sqrt { 288 }$
E)Distances between the points: $\sqrt { 19 } , \sqrt { 200 } , \sqrt { 288 }$

Quizplus · Accepted Answer

To form an isosceles triangle, two sides must be of equal length. Calculating the distances between the points using the distance formula $\sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}$, we find that two distances are equal ($\sqrt{200}$) and one is different ($\sqrt{288}$), matching option B. This indicates that the triangle formed by these points is indeed isosceles.

Show That the Points Form the Vertices of the Indicated 37,200,288\sqrt { 37 } , \sqrt { 200 } , \sqrt { 288 }37​,200​,288​

Show That the Points Form the Vertices of the Indicated $\sqrt { 37 } , \sqrt { 200 } , \sqrt { 288 }$