We have two straight lines AB and CD. The coordinates of A,B and C are A(1,3), B(5,9) and C(0,8). The point D lies on the line AB and is halfway between points A and B. Is the line CD perpendicular to AB?

First of all we need to find the coordinates of the point D. As D is halfway between the two points A and B, to find the midpoint of a line segment, we add the x coordinates then divide by 2, and add the y coordinates and divide by 2. This gives us D(3,6).To find the gradient of AB, we need to divide the change in the y-coordinate by the change in the x-coordinate. (9-3)/(5-1) =3/2 so 3/2 is the gradient of the line segment AB. As we now know our D coordinates we can work out the gradient of CD. (8-6)/(0-3)=-2/3 which is the gradient of line segment CD.If two lines are perpendicular to one another then: (gradient of AB) x (gradient of CD) = -1We then check this : 3/2 x -2/3 = -1 . So AB and CD are indeed perpendicular.

Answered by Bryony H. Maths tutor

4718 Views

See similar Maths GCSE tutors

Related Maths GCSE answers

All answers ▸

What is Pythagoras' Theorem and how do you use it?


Prove n^3-n is multiple of 6 for all n


A is (2, 12) and B is (8, 2) Calculate the midpoint of AB.


A right-angle triangle has sides AB, BC and CA with the right -angle between sides BC and CA. The angle between AB and BC is 24 degrees. The length of AB is 12m. How long is side BC?


We're here to help

contact us iconContact usWhatsapp logoMessage us on Whatsapptelephone icon+44 (0) 203 773 6020
Facebook logoInstagram logoLinkedIn logo
Cookie Preferences