Question 3 (25 marks)
(a) The co-ordinates of two points are A(4, 1) − and B(7, t).
The line

is perpendicular to AB. Find the value of t.

(b) Find, in terms of k, the distance between the point P (10,k ) and

(c) P (10,k ) is on a bisector of the angles between the lines

and

(i) Find the possible values of k.
(ii) If k > 0, find the distance from P to

Question 1 (25 marks)
The points A(6, −2), B(5, 3) and C(‒3, 4) are shown on the diagram.
(a) Find the equation of the line through
B which is perpendicular to AC.

b) Use your answer to part (a) above to find the co-ordinates of the orthocentre of the
triangle ABC.

Question 5 (25 marks)
The line m: 2x+3y+1=0 is parallel to the line ݊n:2x+3y-51=0
(a) Verify that A(-2,1) is on ݉m

(b) Find the coordinates of B, the point on the line ݊n closest to A, as shown below.

Question 2 (25marks)
(a) Theline 𝑝 makes an intercept on the 𝑥-axis at (a, 0) and on the 𝑦-axis at (0, 𝑏),
where

Show thatthe equation of 𝑝 can be written as

(b) Theline 𝑙 has a slope 𝑚, and contains the point 𝐴(6, 0)
(i) Write the equation of the line l in terms of m

Question 1 (25 marks)
(a) The coordinates of three points are 𝐴(2, −6), 𝐵(6, −12), and 𝐶(−4, 3).
Find the perpendicular distance from 𝐴 to 𝐵𝐶.
Based on your answer, what can you conclude about the relationship between
the points 𝐴, 𝐵, and 𝐶?