Question

0. Two lines AB and AC pass through the points A(4, 3), B(6, 0) and A(4, 3), C(-1,0). By forming simultaneous equations using the equation of the line y = mx + c, find the equation of AB and AC. Write each equation in the form ax + by + c = 0, where a, b, c e Z. Show that the point A(4, 3) is on both lines.​

Answer 1

Explanation:

A

(y-3)/(0-3) = (x-4)(6-4)

(y-3)/-3 = (x-4)/2

(-y+3)/3 = (x-4)/2

6 *(-y+3)/3 = 6 * (x-4)/2

-2y + 6 = 3x - 12

-3x -2y + 6 + 12 = 0

-3x - 2y + 18 = 0

3x + 2y - 18 = 0

Verify point A

3(4) + 2(3) - 18 = 0

12 + 6 - 18 = 0

0 = 0 (ok)

B

(y-3)/(0-3) = (x-4)/(-1-4)

(y-3)/-3 = (x-4)/-5

-15 * (y-3)/-3 = -15 * (x-4)/-5

5y-15 = 3x - 12

3x - 5y - 12 + 15 = 0

3x - 5y + 3 = 0

Verify point A

3(4) - 5(3) + 3 = 0

12 - 15 + 3 = 0

0 = 0 (ok)