Question

prove that the points (7,10),(-2,5),(3,-4) are the vertices of an isosceles right triangle

Answer 1

Answer:

Step-by-step explanation:

A(7,10) B(-2,5) C(3,-4) Use the distance formula to find the length of the sides.

d = √[(x2-x1)2 + (y2-y1)2]

AB = √[(-2-7)2 + (5-10)2

AB = √[(-9)2 + (-5)2

AB = √[81 + 25] = √106

BC = √[(3+2)2 + (-4-5)2]

BC = √[52 + (-9)2]

BC = √[25 + 81] = √106 Thus, AB = BC

m = (y2 - y1)/x2 - x1

mAB =(5-10)/((-2-7) = -5/-9

mAB = 5/9

mBC = (-4-5)/(3+2)

mBC = -9/5 Since the slopes of AB and BC are negative reciprocals of each other, AB⊥BC.

Thus ∠B is a right angle. Since AB = BC, ΔABC is a right, isosceles triangle.

Answer 2

Hence, A,B and C are the vertices of isosceles right angle triangle