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.

BH
Answered by Bryony H. Maths tutor

5537 Views

See similar Maths GCSE tutors

Related Maths GCSE answers

All answers ▸

For the equation 7x+3y=10x/y make x the subject.


If a train leaves for a 130 mile journey at 1.30pm, and travels at a constant speed of 50 miles per hour, at what time will it arrive?


Simplify 8x-3+6x


c) Sharon is organising an event. The tickets cost 12 pounds each. Sharon paid 200 pounds for the cost of the event. How many tickets will Sharon have to sell to make a profit? (2 marks)


We're here to help

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

© MyTutorWeb Ltd 2013–2025

Terms & Conditions|Privacy Policy
Cookie Preferences