Question

20 points One diagonal of a rhombus has endpoints (-10, 1) and (2, 9).

What are the endpoints of the other diagonal?

(-7, 7) and (-1, 3)
(-4, 7) and (2, 7)
(-2, 2) and (-6, 8)
(-6, 2) and (-2, 8)

Answer 1

Check the picture below.

so as you already know, a rhombus is a parallelogram whose sides are equal, so the distance from say (-10, 1) to either endpoint of the other diagonal must be the same.

`\bf ~~~~~~~~~~~~\textit{distance between 2 points} \\\\ (\stackrel{x_1}{-10}~,~\stackrel{y_1}{1})\qquad \underline{(\stackrel{x_2}{-2}~,~\stackrel{y_2}{2})}\qquad \qquad d = √(( x_2- x_1)^2 + ( y_2- y_1)^2) \\\\\\ d=√([-2-(-10)]^2+[2-1]^2)\implies d=√((-2+10)^2+(2-1)^2) \\\\\\ d=√(64+1)\implies \boxed{d=√(65)} \\\\[-0.35em] ~\dotfill`

`\bf (\stackrel{x_1}{-10}~,~\stackrel{y_1}{1})\qquad \underline{(\stackrel{x_2}{-6}~,~\stackrel{y_2}{8})}\qquad \qquad d=√([-6-(-10)]^2+[8-1]^2) \\\\\\ d=√((-6+10)^2+(8-1)^2)\implies d=√(16+49)\implies \boxed{d=√(65)}`

Answer 2

(-10, -8) and (-6, -4)

Explanation: