Coordinate geometry (distance, midpoint, gradient) — KCSE Mathematics

KCSE Mathematics · 137 practice questions · 4 syllabus objectives

46 easy46 medium45 hard

What You'll Learn

Key learning outcomes for this topic, aligned to the KNEC KCSE syllabus.

Calculate the distance between two points, the midpoint of a line segment and the gradient of a line

Write the equation of a straight line in the form y = mx + c and ax + by + c = 0; find the equation given gradient and a point, or two points

Determine whether two lines are parallel or perpendicular from their gradients; find the equation of a line perpendicular to a given line

Coordinate geometry (distance, midpoint, gradient)

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easySHORT ANSWER2 marks

Calculate the distance between the points P(-1, -2) and Q(7, 3). Leave your answer in surd form where necessary.

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Part (a) — 2 marks

Distance = √[(7 − -1)² + (3 − -2)²] (1 mk)

Simplify the surd where possible (1 mk)

easySHORT ANSWER2 marks

Find the coordinates of the midpoint M of the line segment joining A(2, 1) and B(-1, 10).

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Part (a) — 2 marks

M = ((2 + -1)/2, (1 + 10)/2) (1 mk)

State the midpoint coordinates (1 mk)

easySHORT ANSWER2 marks

For the straight line equation 4y = -4x + -8, determine the coordinates of the points where the line meets the x-axis and the y-axis.

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Part (a) — 2 marks

y-intercept: set x = 0 → 4y = -8 → y = -8/4; point is (0, -8/4) (1 mk)

x-intercept: set y = 0 → 0 = -4x + -8 → x = −-8/-4; point is (−-8/-4, 0) (1 mk)

A straight line L₁ has a gradient of 2/3 and passes through the point (-3, -1). Find its equation in the form y = mx + c.

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