More Maths Home Work?

Question

1. Prove that the three points P(-7,-5), Q(-1,-2) and R(9,3) are collinear?

2. If G(-1,6) h(1,2) and J(5,9) show that GH And GJ are perpendicular?

Please write in full to show how you got the answer thanks.

Answer 1

1. To prove that the points are collinear, you can join two sets of points and show that one is a scalar of the other. So, for example PQ = (6, 3), PR = (16, 8). Note that PR = (8/3)*PQ. Therefore they are collinear.

2. GH and GJ are perpendicular if their dot product is equal to 0. GH = (2, -4), GJ = (6, 3), and GH dot GJ = 2*6 - 4*3 = 0. Therefore they are perpendicular.

Answer 2

slope PQ = [-2 - -5]/[-1 - -7] = 3/6 = 1/2
slope PR = [3 - -5]/[9 - -7] = 8/16 = 1/2
lines with the same slope are parallel.
parallel lines through the same point are just 1 line.

slope GH = [2-6]/[1 - -1] = -4/2 = -2
slope GJ = [9-6]/[5 - -1] = 3/6 = 1/2

perpendicular lines have slopes whose product is -1: -2(1/2) = -1