Question

show that the points A(-1,-2), B(4,3),C(2,5),D(-3,0) on that form of rectangle.
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Answer 1

Answer

Distance between two points can be found using Distance Formula :

$\sf{\sqrt{\left(x_{2}-x_{1}\right)^{2}+\left(y_{2}-y_{1}\right)^{2}}}$

$\textsf{Distance between AB = } \sf{\:\sqrt{\left(4-(-1)\right)^{2}+\left(3-(-2)\right)^{2}}}\:\sf{=\:5\sqrt{2}}$

$\textsf{Distance between BC = } \sf{\:\sf{\sqrt{\left(2-4\right)^{2}+\left(5-3\right)^{2}}}}\:\sf{=\:2\sqrt{2}}$

$\textsf{Distance between CD = } \sf{\:\sf{\sf{\sqrt{\left(-3-2\right)^{2}+\left(0-5\right)^{2}}}}}\:\sf{=\:5\sqrt{2}}$

$\textsf{Distance\:between\:DA\:=\:}\:\sf{\:\sf{\sf{\sqrt{\left(-3-(-1)\right)^2+\left(0-(-2)\right)^2}}}}\:\sf{=\:2\sqrt{2}}$

• Since the Opposite Sides are Equal, We showed That the given points form a rectangle/vertices of Rectangle