Question

*(b) Show that, if A(0,0), B(0, 10), C(8, 16)
and D(8, 6) are the four points then
ABCD is a rhombus. Find the lengths of
the diagonals of the rhombus.​

Answer 1

Given:-

• Points of a Rhombus ABCD are as follows A(0,0), B(0,10), C(8,16) & D(8,6).

To Find:-

• Length of the Diagonals of the Rhombus.

Solution:-

Diagonals of the Rhombus are AC & BD

$\boxed{\sf{☆\; Distance\; between\; two\;points = \sqrt{(x_2-x_1)²+(y_2-y_1)²}\;units}}$

☞ AC

$→\;{\sf{\sqrt{(8-0)²+(16-0)²}}}$

$→\;{\sf{\sqrt{8²+16²}}}$

$→\;{\sf{\sqrt{320}}}$

$→\;{\bf{8\sqrt{5}}}$

• Length of AC = 8√5 units

☞ BD

$→\;{\sf{\sqrt{(8-0)²+(6-10)²}}}$

$→\;{\sf{\sqrt{8²+(-4)²}}}$

$→\;{\sf{\sqrt{80}}}$

$→\;{\bf{4\sqrt{5}}}$

• Length of BD = 4√5 units

$\Large{\pink{\sf{@bharti046࿐}}}$

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