(a) Define the slope of a straight line joining two distinct points in the Cartesian…
MATHEMATICS · Subjective · A Level · Mathematics · Coordinate geometry in the (x y) plane · Coordinate geometry in the (x y) plane
Problem
(a) Define the slope of a straight line joining two distinct points in the Cartesian plane.
(b) Without performing any numerical calculation, predict whether the slope of the line passing through the points A(2,5) and B(7,1) is positive, negative, zero, or not defined. Give a brief reason based on the relative positions of the two points.
(c) Draw four separate rough sketches of straight lines on the same set of axes to illustrate each of the following cases and label them clearly:
(i) positive slope,
(ii) negative slope,
(iii) zero slope,
(iv) slope not defined.
Explain in two or three sentences for each sketch how the sign or nature of the slope is reflected in the orientation of the line.