Straight line graphs

The points P and Q have coordinates (6, 15) and (12, 19) respectively.

Find the coordinates of the midpoint of PQ

Find the equation of the perpendicular bisector of PQ

Give your answer in the form ax by c where a, b and c are integers.

A circle passes through the points P and Q

The centre of the circle lies on the line with equation 2x 5y 30

Find the equation of the circle.

The circle intersects the coordinate axes at n points.

State the value of n

The lines L₁ and L₂ are parallel.

L₁ intersects the y-axis at the point P.

The point Q is the point on L₂ closest to P, as shown in the diagram.

Find the coordinates of Q.

Hence show that PQ k34, where k is an integer to be found.

A circle, C, has centre (a, 17).

L₁ and L₂ are both tangents to C.

Find a.

Find the equation of C.

The line L has equation

The point P has coordinates (15, 2)

Find the equation of the line perpendicular to L which passes through P.

Hence, find the shortest distance from P to L.

The point A has coordinates (1, a) and the point B has coordinates (3, b)

The line AB has equation 5x 4y 17

Find the equation of the perpendicular bisector of the points A and B.

Three points A, B and C have coordinates A (8, 17), B (15, 10) and C (2, 7)

Show that angle ABC is a right angle.

A, B and C lie on a circle.

Explain why AC is a diameter of the circle.

Determine whether the point D (8, 2) lies inside the circle, on the circle or outside the circle.

Fully justify your answer.

The line L has equation 2x 3y 7

Which one of the following is perpendicular to L ?

Tick one box.