Question

The coordinates of the vertices of a rectangle are L ( -2,6 ), A (10,6), N(10,-3) and D ( -2,-3 ). What is the length of a diagonal of the rectangle?​

Answer 1

$\Large{\underline{\bf{Given:}}}$

☞ LAND is a Rectangle

☞ Points (Vertices) of the Rectangle are follows

❥ L (-2,6) ➝ (a,b)

❥ A (10,6) ➝ (c,d)

❥ N (10,-3) ➝ (e,f)

❥ D (-2,-3) ➝ (g,h)

$\huge{\underline{\bf{To\;Find:}}}$

☞ Length of the Diagonals of the Rectangle.

$\huge{\underline{\sf{Solution:}}}$

In Rectangle LAND → LN & AD are diagonals

W.K.T

The Distance Between Two Points A & B is denoted as $\bf{\bar{AB}}$

$\boxed{\sf{d=\sqrt{(x_2-x_1)²+(y_2-y_1)²}}}$

In LN → L = (X1, Y1) & N = (X2, Y2)

$→\;{\sf{\bar{LN} = \sqrt{(10-(-2))²+(-3-6)²}}}$

$→\;{\sf{\bar{LN} = \sqrt{(10+2)²+(-9)²}}}$

$→\;{\sf{\bar{LN} = \sqrt{(12)²+(-9)²}}}$

$→\;{\sf{\bar{LN} = \sqrt{144+81}}}$

$→\;{\sf{\bar{LN} = \sqrt{225}}}$

$→\;{\sf{\bar{LN} = \sqrt{15²}}}$

$→\;{\sf{\bar{LN} = 15}}$

$\huge{\green{\underline{\underline{\mathfrak{AnSweR:}}}}}$

☞ In a Rectangle Diagonals are equal and bisect each other.

So, The Length of Diagonals LN & AD are

◕➜ $\huge{\red{\mathfrak{15cm}}}$

Hope It Helps You ✌️