Question

Points ABC forms a right triangle.

Answer 1

The sum of squares of the lengths  of the triangle is 130 and the square of the length of the hypotenuse is 65

What is a right-angled triangle?

This is a triangle with 3 sides and one side is called the hypotenuse which faces one of the angles 90°

Analysis:

distance between two points = $\sqrt{(x2 - x1)^{2} + (y2 - y1)^{2} }$

distance AB with coordinates A(-2,4) B(5,0) = $\sqrt{(5 - -2)^{2} + (0 - 4)^{2} }$ = $\sqrt{65}$

distance AC with coordinates A ( -2,4) C(2,6) = $\sqrt{(2--2)^{2} + (6-4)^{2} }$ = $\sqrt{20}$

distance BC with coordinates B(5,0)  C(2,6) = $\sqrt{(2-5)^{2} + (6-0)^{2} }$ = $\sqrt{45}$

sum of squares of the lengths = $(\sqrt{45} )^{2}$ + $(\sqrt{65}) ^{2}$ + $(\sqrt{20}) ^{2}$ = 65 + 45 + 20 = 130

the square of the length of the hypotenuse = 65

In conclusion, the sum of the squares of the three length is 130 and the square of the hypotenuse is 65

Learn more about right-angled triangle: brainly.com/question/64787

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