prove that these cooridants are of isosceles triangle
A = ( 7 , 10)
B = (-2, 5 )
C = ( 3 , - 4)
Answers
Answer:
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:
We need to prove that the coordinates are of an isosceles triangle. To do so we need to use the distance formula to find the length of the sides.
Explanation:
Length of AB = √(x² - x¹)² +( y² - y¹)²
√ 4 - 49 + 25 - 100
√ - 45 - 75
√-120 units
Length of BC = √(x² - x¹)² +( y² - y¹)²
√ 9 - 4 + 16 - 25
√ 5 - 9
√- 4 units
Length of CA = √(x² - x¹)² +( y² - y¹)²
√ 49 - 9 + 100 - 16
√ 40 + 74
√114 units
Since none of the coordinates matches with each other therefore these are not the coordinates of isosceles triangle.
I think there is a problem with the question. I hope you will understand the procedure and can implement in other questions.