# A (-1, 0), B (1, 3) and D (3, 5) are the vertices of a parallelogram ABCD. Find the co-ordinates of vertex C. - Mathematics

Sum

A (-1, 0), B (1, 3) and D (3, 5) are the vertices of a parallelogram ABCD. Find the co-ordinates of vertex C.

#### Solution

Let the co-ordinates of vertex C be (x, y).
ABCD is a parallelogram.
∴ Mid-point of AC = Mid-point of BD

((-1+x)/2,(0+y)/2)=((1+3)/2,(3+5)/2)

((-1+x)/2,y/2)=(2,4)

(-1+x)/2=2 and y/2=4

x=5 and y/2=4

x=5 and y=8

Thus, the co-ordinates of vertex C is (5, 8).

Concept: The Mid-point of a Line Segment (Mid-point Formula)
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#### APPEARS IN

Selina Concise Maths Class 10 ICSE
Chapter 13 Section and Mid-Point Formula
Exercise 13 (B) | Q 12 | Page 182