Question

A (14, – 2), B (6, – 2) and D (8, 2) are the vertices of a parallelogram ABCD. Find the coordinates of the vertex C. Also find the length of diagonal BD.

Answer 1

Answer:

Step-by-step explanation:The diagoanls of a parrelogram bisect each other. Lets say that they bisect at O .

O is the midpoint of AC

coordiantes of O = (6+8)/2 , (-2+2)/2

USING MID POINT FORMULA

coordinates of O = (7,0)

Since O is also the mid point of BD

again using MID POINT FORMULA

O= (14+x)/2 , (-2+y)/2.

coordinates of c=(x,y)

7= 14+x÷2 and 0 = -2+y÷2

x=0. y=2

coordinates of C = (0,2)

length of BD = [(8-6)^2 + (2+2)^2]^1/2

= [ 4 +4 ] ^1/2

= 8^1/2

= 2 × 2^1/2