The endpoints of the other diagonal are (-2, 2) and (-6, 8).
Distance formula, Algebraic expression that gives the distances between pairs of points in terms of their coordinates (see coordinate system). In two- and three-dimensional Euclidean space, the distance formulas for points in rectangular coordinates are based on the Pythagorean theorem.
Given we have a rhombus with endpoints (-10, 1) and (2, 9)
So as we 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.
Distance between 2 points [tex]$\mathrm{d}=\sqrt{[-2-(-10)]^2+[2-1]^2} \Longrightarrow d=\sqrt{(-2+10)^2+(2-1)^2}$\mathbf{d}=\sqrt{\mathbf{6 4 + 1}} \Longrightarrow d=\sqrt{65}$[/tex]
While solving with other coordinate we get [tex]$\mathbf{d}=\sqrt{(-6+10)^2+(8-1)^2}[/tex]
[tex]$\mathrm{d}=\sqrt{16+49}\\\Longrightarrow d=\sqrt{65}$[/tex]
So therefore the endpoints of the other diagonal are (-2, 2) and (-6, 8) .
To learn more about parallelogram visit brainly.com/question/12823094
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