Question

Plot the points A(1,0),B(4,0),C(1,3) find the coordinates of D such that ABCD is a square *

Answer 1

Answer:

(-2,3)

Step-by-step explanation:

Let A(1,0), B(4,0), C(1,3), D(x₄,y₄) be the vertices of the square ABCD.

In a square,the diagonals bisect each other.

i,e, mid-point of AC=mid-point of BD

⇒(x₁+x₃/2 , y₁+y₃/2)=(x₂+x₄/2 , y₂+y₄/2)

⇒ (1+1/2 , 0+3/2) = (4+x₄/2, 0+y₄/2)

⇒ (1, 3/2)=(4+x₄/2, 0+y₄/2)

∴ 4+x₄/2=1 (∵corresponding x-coordinates)

⇒ 4+x₄=2

⇒ x₄= -2

And, 0+y₄/2=3/2 (∵corresponding y-coordinates)

⇒ 0+y₄=3

⇒ y₄=3

Hence, the required co-ordinates of D is (-2,3).