Question

Let A = (-4,0), B = (-1,4). C and D are
points which are symmetric to points A
and B respectively with respect to y-axis,
then the area of the quadrilateral ABDC
is​

Answer 1

Given:

Let A = (-4,0), B = (-1,4). C and D are points which are symmetric to points A and B respectively with respect to y-axis, then the area of the quadrilateral ABDC is​

To find:

The area of the quadrilateral ABDC is​

Solution:

From given, we have,

A = (-4, 0), B = (-1, 4).  

As C and D are points which are symmetric to points A and B respectively with respect to the y-axis,

Then the values of C and D are same as the values of A and B, with opposite sign of x-axis:

C = (1, 4), D = (4, 0).

Consider the attached figure while going through the following steps.

Area of quadrilateral = (a + b)/2 h

from given, we have,

a = 2, b = 8 and h = 4.

Therefore, the area of the quadrilateral is,

Area of quadrilateral = (2 + 8)/2 × 4 = 10/2 × 4 = 5 × 4 = 20

∴ The area of the quadrilateral ABDC is​ 20 sq units

Answer 2

given the area of quadrilateral ans .20