Coordinate Geometry — Solutions

Full worked solutions, with method and final answer for every part.

Question 1

(a)Gradient = (y₂ − y₁)/(x₂ − x₁) = (10−2)/(7−1).

4/3

Question 2

(a)Midpoint = ((x₁+x₂)/2, (y₁+y₂)/2) = ((1+7)/2, (2+10)/2).

(4, 6)

Question 3

(a)Use Pythagoras: AB = √[(x₂−x₁)² + (y₂−y₁)²] = √(6² + 8²) = √100.

AB = 10

Question 4

(a)Gradient = (y₂−y₁)/(x₂−x₁) = (−5−3)/(4−(−2)).

−8/6 = −4/3

Question 5

(a)Midpoint = ((x₁+x₂)/2, (y₁+y₂)/2).

(1, −1)

Question 6

(a)AB = √[(x₂−x₁)² + (y₂−y₁)²] = √(6² + 8²).

√100 = 10

Question 7

(a)y = mx + c, with m = 2 and c = 4 (the y-intercept given).

y = 2x + 4

(b)Substitute x = 3.

y = 2(3)+4 = 10

Question 8

(a)The x-coordinates are equal, so the change in x is zero — division by zero is undefined.

The line is vertical, so the gradient is undefined

Question 9

(a)Substitute x=3 into the line equation and check the result equals 5.

2(3)−1 = 5, which matches, so the point lies on the line

Question 10

(a)Use Pythagoras: √(6²+8²).

√100 = 10

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