Question

In the diagram,

B (5,9)
A (2,3)
the points A, B and C lie on the straight line y = 2x-1
The coordinates of A are (2, 3).
The coordinates of B are (5, 9).
Given that AC = 3AB, find the coordinates of C.
0
y=2x+1
C

Answer 1

C = (11, 21)

Explanation:

The relation AC = 3AB can be used to find the coordinates of C given those of A and B.

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C -A = 3(B -A)

C = 3B -2A . . . . . add A to both sides

C = 3(5, 9) -2(2, 3) = (15 -4, 27 -6) . . . . use the given points for A and B

C = (11, 21)