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ABCD is a parallelogram with A(1,1) and C(8, 10). The equation of AB is 4x - 5y = -1 and the equation of BC is 5x - 2y = 20. Determine

ABCD is a parallelogram with A(1,1) and C(8, 10). The equation of AB is 4x - 5y = -1 and the equation of BC is 5x - 2y = 20. Determine
a) The coordinates of M, where M is the midpoint of intersection of the diagonals
b) The coordinates of the vertices B and D

Answers

John
a) M is the midpoint

($\frac{8 + 1}{2}$), $\frac{10 + 1}{2}$

M (4.5, 5.5)

b) Co -ordinate of B

(4x - 5y = -1)2
(5x - 2y = 20)5

8x - 10y = -2
25x - 10y = 100

17x = - 102; x = 6

4(6) - 5y = -1

24 - 5y = -1

-5y = -25;y = 5, B (6, 5)

Co -ordinate of D

4.5 = $\frac{c + 6}{2}$; 9 = C + 6

c = 3

5.5 = $\frac{d + 5}{2}$

11 = d + 5;

d = 6

D(3, 6)

johnmulu answered the question on March 2, 2017 at 12:07

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