Theory question 115
Vectors and Transformations(a) P(7, 4) is a vertex of triangle PQR. If QP = (3, 5) and PR = (−3, 4), find: (i) the co-ordinates of Q; (ii) PN where N is the midpoint of QR.
(b) A straight line passes through the points (1, 4) and (3, 0). Find the (i) gradient; (ii) equation of the line.
Show the model answer
Model answer
(a)(i) Q = P − QP = (7 − 3, 4 − 5) = (4, −1).
(ii) R = P + PR = (4, 8). N = midpoint of QR = (4, 3.5). PN = (4 − 7, 3.5 − 4) = (−3, −0.5).
(b)(i) Gradient = (0 − 4)/(3 − 1) = −2.
(ii) y − 4 = −2(x − 1) → y = −2x + 6.
Explanation
A vector QP = (position of P) − (position of Q).