Show that points (7,10) , (-2,5) , (3,-4) are the vertices of an isosceles right triangle.
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Step-by-step explanation:
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Secondary School Math 5 points
Prove that the points (7,10),(-2,5),(3,-4) are the vertices of an isosceles right triangle
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gaurkhushi2136 Helping Hand
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.