Question

The coordinates of point A are (-4, p) and the coordinates of point B are ( 2, -3 ).
The mid-point of the line segment AB, has coordinates ( q, 1).
(a) Find the value of
(i) q
(ii) p
(b) Calculate the distance AB.

Answer 1

So are you aware of mid point formula?

Answer 2

yes

Answer 3

Ok. So mid point of AB is (q,1)

Hence (-4+2/2, p-3/2) = (q,1)

=> (-1, p-3/2) = (q,1)

so q = -1, and p = 5. (on solving)

Hence A = (-4, 5) B = (2,-3)

U can use distance formula to solve for AB.

Do it yourself.(the answer should be 10 units.)

Answer 4

so, if the midpoint formula says to add the x coordinates together and divide by 2, then add the y coordinates and divide by 2 in order to get the mid point. So we have (-4+2)=-2, then we divide by 2 to get -1, giving us the x value for the midpoint. For the Y value, we have (P-3) all divided by 2= the y value of 1 (given by the coordinate (q,1)). So, (P-3)/2=1. Multiply both sides by 2, and add 3 to find that p=5

Answer 5

thank you both so much for the answers, that really clears things up!