Question

Please answer it fast

Answer 1

Answer:

(a) The co-ordinates of fourth vertex D ≡ (4,-1).

(b) The mid-point of BC ≡ (3,7).

(c) The point of intersection of the diagonals ≡ (3,3).

Step-by-step explanation:

Mid-point of line joining two points (x₁,y₁) and (x₂,y₂) ≡ ($\frac{x_{1}+x_{2}}{2},\frac{y_{1}+y_{2}}{2}$).

⇒Mid-point of BC ≡ ($\frac{2+4}{2},\frac{7+7}{2}$) ≡ (3,7)

The mid-point of diagonal AC ≡ ($\frac{2+4}{2},\frac{-1+7}{2}$) ≡ (3,3).

(3,3) is also the point of intersection of the diagonals. This is because diagonals of a rectangle bisect each other at their mid-points.

⇒ (3,3) is also the mid-point of diagonal BD.

⇒If (x₁,y₁) are the co-ordinates of point D, then mid-point of BD = ($\frac{2+x_{1}}{2},\frac{7+y_{1}}{2}$) = (3,3).

⇒ x₁ = 4 and y₁ = -1.

⇒Co-ordinates of point D ≡ (4,-1).