Question

Haresh is writing a coordinate proof involving an isosceles triangle. Haresh places his triangle on the coordinate plane such that the base of the triangle lies along the x-axis.
What coordinates should he assign to this third vertex of the isoceles triangle?



(2a, b)

(a/2, b/2)

(a/2, b)

(b, 2b)

Answer 1

Answer:- (a/2, b) is coordinates should he assign to the third vertex of the isosceles triangle.

Explanation:-

As the given triangle is isosceles then the median of the triangle divides it into two equal triangles such that the base of the new triangles becomes half of the original triangle$=\frac{1}{2}a$      

 [where a is the base of the original isosceles triangle]

Since the median of the given triangle join the third vertex and the mid point of the base thus the x coordinate of the points remains same$=\frac{1}{2}a$ and from the graph it is clear that y coordinate of third point is b .

Thus the coordinates for the third vertex must be $(\frac{a}{2},b)$.

Answer 2

(a/2,b)

Hope this helps!