IGCSE Maths Coordinate geometry topical questions

A line passes through (0, 1) and (2, 5).

1. (a)Find the gradient of the line.[2]
2. (b)Write down the y-intercept.[1]

The line is y = 5 − 2x.

1. (a)State the gradient of the line.[1]
2. (b)Show that the point (3, −1) lies on the line.[1]
3. (c)Find the x-intercept of the line.[2]

P(−3, −2) and Q(5, 4).

1. (a)Find the gradient of the segment PQ.[2]
2. (b)Find the coordinates of the midpoint of PQ.[1]
3. (c)Find the length of PQ.[2]

A line has equation 3x + 4y = 24.

1. (a)Find the y-intercept of the line.[1]
2. (b)Find the x-intercept of the line.[1]
3. (c)Find the gradient of the line.[2]
4. (d)Does the point (2, 4) lie on the line? Show how you decide.[1]

A(1, 3) and B(7, 6). (Extended)

1. (a)Find the gradient of AB.[2]
2. (b)Find the exact length of AB.[2]
3. (c)Write down the midpoint of AB.[1]

A line has gradient 3 and passes through (2, 1).

1. (a)Find the equation of the line.[2]
2. (b)Show that the point (4, 7) lies on the line.[1]
3. (c)Write down the coordinates of the y-intercept.[1]

The line l is y = 2x + 1. (Extended)

1. (a)Write down the gradient of any line perpendicular to l.[1]
2. (b)Find the equation of the line through (4, 3) perpendicular to l.[3]
3. (c)Find the x-coordinate of the intersection of the two lines.[1]

The segment joins (0, 2) and (6, 8). (Extended)

1. (a)Find the midpoint of the segment.[2]
2. (b)Find the gradient of the segment.[1]
3. (c)Find the equation of the perpendicular bisector of the segment.[2]

The segment AB joins A(2, 3) to B(6, 11). (Extended)

1. (a)Find the gradient of AB.[2]
2. (b)Find the equation of the perpendicular bisector of AB.[4]

A(−1, 0), B(3, 6) and C(9, 2). (Extended)

1. (a)Show that angle ABC is a right angle.[3]
2. (b)Find the length of the shortest side, giving your answer in exact surd form.[3]

Line p passes through (1, 4) and is parallel to the line 2x + y = 9.

1. (a)Find the gradient of the line 2x + y = 9.[2]
2. (b)Find the equation of line p.[2]
3. (c)Find the x-intercept of line p.[1]

A(−1, 2), B(3, 10) and C(7, 18). (Extended)

1. (a)Find the gradient of AB.[1]
2. (b)Find the gradient of BC.[1]
3. (c)State what parts (a) and (b) show about the three points.[1]
4. (d)Find the exact length of AC.[2]
5. (e)Find the midpoint of AC and comment on your answer.[1]

l₁ is the line y = 2x + 1 and l₂ is the line y = −x + 7. (Extended)

1. (a)Solve the two equations simultaneously to find where l₁ and l₂ cross.[3]
2. (b)Find the gradient of any line perpendicular to l₁.[1]
3. (c)Find the equation of the line through the intersection point that is perpendicular to l₁.[2]

On a map grid, towns sit at A(0, 0), C(3, 4) and B(6, 8), with one grid unit equal to one kilometre. (Extended)

1. (a)Show that C lies on the straight road from A to B, and is in fact the midpoint of AB.[3]
2. (b)Find the length of AB.[1]
3. (c)A walker hikes from A to C at 4 km/h. How many minutes does this leg take?[2]