Question

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Solve this please :- 7th one with full explanation!

Answer 1

$\bold{Given,}$

A RECTANGLE HAS VERTICES AOBC.

$\bold{Coordinates \: of \: A(0,3) as (x_1 , y_1)}$

$\bold{Coordinates \: of \: O(0,0)as (x_2 , y_2)}$

$\bold{Coordinates \: of \: B(5,0)as (x_3 , y_3)}$

$\bold{Coordinates \: of \: C as (x_4, y_4)}$

Since, diagonals of rectangle bisect each other .Let the point of intersection be P

AP = PB

So, to find coordinates of P

Apply mid point theorem ,

FOR x,

$\bold{ x =\frac{x_1 + x_2}{2}}$

$\bold{ x =\frac{0 + 5}{2}}$

$\boxed{ x = 2.5}$

FOR y,

$\bold{ y=\frac{y_1 + y_2}{2}}$

$\bold{ y =\frac{3 + 0}{2}}$

$\boxed{ y = 1.5}$

We since P is bisector of both diagonals

therefore OP=OC

So, for coordinates of C.

Apply mid point theorem ,

FOR x,

$\bold{ x =\frac{x_2 + x_4}{2}}$

$\bold{ 2.5 =\frac{0 + x_4}{2}}$

$\boxed{ x = 5}$

FOR y,

$\bold{ y=\frac{y_1 + y_4}{2}}$

$\bold{ 1.5 =\frac{0+ y_4}{2}}$

$\boxed{ y = 3}$

So, the coordinates of C are $\bold{(5,3)}$