Question

Plot the following points on a graph and answer the following questions: (2 , 3) ( 6 , 3) (8 , 8) (4 , 8) a) Which figure is formed ?
b) Find the area of the figure so formed.​

Answer 1

$\large\underline{\sf{Solution-}}$

Given coordinates are (2 , 3) ( 6 , 3) (8 , 8) (4 , 8)

Let us assume that

↝ Coordinates of A be (2, 3)

↝ Coordinates of B (6, 3)

↝ Coordinates of C (8, 8)

↝ Coordinates of D (4, 8).

[ Please see the attachment ].

From graph we concluded that

↝ AB = 4 units

↝ CD = 4 units

We know,

↝ Slope of a line (m) joining two points (a, b) and (c, d) is given by

$\rm :\longmapsto\:\boxed{ \tt{ \: m = \frac{d - b}{c - a} \: }}$

So,

Slope of line AB joining the points A (2, 3) and B (6,3) is

$\rm :\longmapsto\:Slope \: of \: AB = \dfrac{3 - 3}{6 - 2} = \dfrac{0}{4} = 0$

And,

Slope of line CD joining the points C (8, 8) and D (4 8) is

$\rm :\longmapsto\:Slope \: of \:CD = \dfrac{8 - 8}{8 - 4} = \dfrac{0}{4} = 0$

Since, Slope of AB = Slope of CD.

$\bf\implies \:AB \: \parallel \: CD$

It implies, AB = CD = 4 units and AB || CD.

As we know that,

In a quadrilateral, if one pair of opposite sides are equal and parallel, then quadrilateral is a parallelogram.

So, this figure, ABCD is a parallelogram.

From graph, Height of parallelogram = 5 units

Now,

Area of a parallelogram = Base × height = 4 × 5 = 20 square units.