Question

The equation of one of the rectangle is 3x-4y-10=0 and the coordinates of two of its vertices are (-2,1) and (2,4) then ,the area of the rectangle is ????

Answer 1

Answer:

• The area of rectangle = 20 sq.units.

Given :

• Equation of side of rectangle = 3x−4y−10=0.

• The coordinates of two of its vertices are (-2,1) and (2,4).

To find :

• Area of the rectangle =?

Step-by-step explanation :

Equation of side of rectangle = 3x−4y−10=0 [Given]

Points (−2,1) and (2,4) do not lie on the line .

Slope of this line is 3/4

So, the slope of other side (perpendicular side) is −4/3

Equation of side passing through (2,4) and slope − 3/4 is

y - 4 = - 4/3(x - 2)

4x + 3y = 20

Now, length of perpendicular from (−2,1) on line 3x−4y−10=0 is

p1 = ∣−20∣/5 = 4

So, p1 = 4

Length of perpendicular from (−2,1) on line 4x+3y−20=0 is

p2 = ∣−25∣/5 = 5

So, p2 = 5

Area of rectangle = Length × Breadth

Substituting the values in the above formula, we get,

= p1 × p2

= 4 × 5

=20 sq. Unit

Thus, The area of rectangle = 20 sq.units.