Coordinate Geometry (1 Viewer)

[FDownes]

Can anyone help me out with this coordinate geometry question? It asks;

The diagram shwos the points A (-2, 0), B (1, 4) and the point C which lies on the x-axis. D us the midpoint of the interval AC. F is a point on AB such that DF is parallel to BC.

a) Find the gradient of AB.

Easy, the answer is 4/3

b) Find the equation of the line AB

Should be easy, but I end up with 4x - 3y - 8 = 0, whereas the solutions say the answer should be 3x - 3y - 8 = 0...

c) The gradient of the line BC is -3/4. Show that the triangle ABC is right angled.

= Gradient AB * Gradient BC = 4/3 * -3/4
= 4/3 * -3/4 = -1
Therefore AB and BC are perpendicular
Therefore triangle ABC is right angled

d) If the length of BC is 6 and 2/3 units, find the coordinates of the point C.

Not sure how to tackle this one, so from here onwards I haven't completed the questions.

e) Calculate the area of triangle ABC.

f) Find the coordinates of F.

 

[lolokay]

clearly the solution for b) is wrong, since that says the gradient is 1

d) use perpendicular distance formula. We know the y coordinate is 0
|4x - 3y - 8|/[sqrt.a^2+b^2] = 6 2/3
4x+8/5 = 6 2/3
x = 6 1/3 (I think)

you should be able to do the other questions