Question

three vertices of a parallelogram ABCD are (3,-4)B ( -1,-3) and C (-6,2) find the coordinates of vertex D​

Answer 1

Hello,Buddy!!

Given:-

• ABCD is a Parallelogram.
• A(3,-4), B(-1,-3) & C(-6,2)

To Find:-

• Coordinates of Vertex D.

Required Solution:-

In Parallelogram ABCD, AC & BD are diagonals.

WKT

• In a Parallelogram diagonals bisect each other.

Means Midpoint of AC & DB is Same.

Let's, Midpoint of AC be (x,y)

$(x,y) = \frac{3 + (- 6)}{2} ,\frac{( - 4) + 2}{2} \\ (x,y) = \frac{3 - 6}{2} , \frac{ - 4 + 2}{2} \\ (x,y) = \frac{3}{2} , \frac{ - 2}{2} \\ (x,y) = \frac{3}{2} , - 1$

• The Midpoint is (3/2,-1)

$\frac{ - 3}{2} , - 1 = \frac{ - 1 + x}{2} , \frac{ - 3 + y}{2} \\ \frac{ - 3}{2} = \frac{ - 1 + x}{2} , - 1 = \frac{ - 3 + y}{2} \\ ( - 3)2 = 2( - 1 + x) , ( - 1)2 = - 3 + y \\ - 6 = - 2 + 2x , -2 +3 = y \\ - 6 + 2 = 2x , 1 = y \\ x = \frac{ - 4}{2} , y = 1 \\ x = - 2 , y = 1$

• Coordinates of Vertex D ➪ (-2,1)

Formulas Used:-

• Midpoint (x,y) ☞︎︎︎ $\sf{[\frac{x_1+x_2}{2}],[\frac{y_1+y_2}{2}]}$

$\boxed{\tt{@MrSovereign}}$

Hope It Helps You ✌️