Sec 4 E-Math Coordinate Geometry topical questions

Find the distance between (1, 2) and (4, 6).

Find the midpoint of (−3, 5) and (7, −1).

Find the gradient of the line through (2, 3) and (6, 15).

Find the equation of the line with gradient 3 passing through (1, 2).

Find the equation of the line through (0, −2) and (3, 4).

Find the midpoint of (5, −2) and (−1, 8), and the distance between the two points, correct to 3 significant figures.

A line has gradient −1 and passes through (−2, 4). (a) Find its equation. (b) State its x-intercept.

The vertices of a triangle are A(0, 0), B(8, 0) and C(0, 6). (a) Find AB, AC and BC. (b) Find the area of the triangle. (c) Show that the triangle is right-angled.

1. (a)The three side lengths.[2]
2. (b)Area.[1]
3. (c)Right angle.[1]

A line passes through (2, −1) and (6, 7). (a) Find its equation. (b) Write down the coordinates of its x-intercept.

1. (a)Equation.[3]
2. (b)x-intercept.[1]

Find the coordinates of the point where the line y = x + 4 meets the line x + y = 11.

P(1, 1), Q(5, 1), R(7, 4) and S(3, 4) are four points. (a) Show that PQ is parallel and equal in length to SR. (b) Show that PS = QR. (c) State the type of quadrilateral PQRS.

The points (2, 1), (4, k) and (6, 9) are collinear. (a) Find the gradient of the line using the first and third points. (b) Find k. (c) Write down the equation of the line.

1. (a)Gradient.[2]
2. (b)k.[2]
3. (c)Equation.[1]

A(1, 2) and B(7, 10) are two points. (a) Find the midpoint M of AB. (b) Show that AM and MB have the same gradient. (c) Find the length of AB.

1. (a)Midpoint M.[1]
2. (b)Equal gradients.[2]
3. (c)Length AB.[2]

The line ℓ has equation 2x − 3y = 6. (a) State its x-intercept and y-intercept. (b) State its gradient. (c) Find the equation of the line through (3, 1) parallel to ℓ.

1. (a)Intercepts.[2]
2. (b)Gradient.[1]
3. (c)Parallel line.[1]

A line has equation y = 3x − 6. (a) Write down its x-intercept. (b) Write down its y-intercept. (c) Find the distance between the two intercepts, to 3 significant figures. (d) Find the midpoint of the two intercepts.

1. (a)x-intercept.[1]
2. (b)y-intercept.[1]
3. (c)Distance.[2]
4. (d)Midpoint.[1]

A(−1, 2) and B(3, 4) are two points. (a) Find the midpoint of AB. (b) Find the equation of the line AB in the form y = mx + c. (c) Determine whether C(7, 6) lies on the line AB.

1. (a)Midpoint.[2]
2. (b)Equation of AB.[2]
3. (c)Is C on AB?[2]

P(1, 2), Q(4, 6) and R(8, 3) are three points. (a) Find the lengths PQ, QR and PR. (b) Show that angle PQR is a right angle. (c) Find the area of triangle PQR.

1. (a)Three lengths.[3]
2. (b)Right angle at Q.[2]
3. (c)Area.[1]

Towns A(0, 0) and B(8, 6) are joined by a straight road. (a) Find the equation of the road, in the form y = mx + c. (b) A relay station S lies at the midpoint of AB; find its coordinates. (c) A third town C(12, 9) is said to be reachable by the same straight road. Verify the claim.

1. (a)Equation of the road.[2]
2. (b)Midpoint S.[2]
3. (c)Verify the claim.[2]

P is (0, 5) and Q is (6, −3). (a) Find the midpoint M of PQ and the gradient of PQ. (b) Show that the perpendicular bisector of PQ has gradient 3/4 and find its equation.

1. (a)Midpoint and gradient.[2]
2. (b)Perpendicular bisector.[4]

A(1, 2), B(5, 4) and C(3, 8) are the vertices of a triangle. (a) Find the gradients of AB and BC. (b) Show that AB ⊥ BC. (c) Show the triangle is isosceles and find its area.

1. (a)Gradients.[2]
2. (b)Right angle at B.[1]
3. (c)Isosceles and area.[3]