Show that triangle ABC is right-angled where A = (-2,-1), B = (2,1) and C = (1,3).

Find the equation of a line which passes through the point A(-3, 4) and which is parallel to the line 3x + 4y - 15=0.

The points P, Q and R are (5, —3), (-6, I) and (1, 8) respectively. Show that these points form an isosceles triangle.

. Find the point of intersection of the lines x ? 2y = ?5 and 2x + 7y ? 34 = 0

  Find the equation of the line passing passing through the midpoint of the points A(? 3 2, ) and B(1,? )4 and which is perpendicular to line AB .

Find the equation of the line passing at point (6, ­2) and it is perpendicular to the line that crosses the ­x-axis at 3 and the y­-axis at ­4.

Let P and Q be two points at (2,5) and (4, -1) respectively. Find

(i)Find equation of the line that passes through the midpoint of PQ and is perpendicular to it in form of ax + by +c=0

(ii)The distance between P and Q

Find the length of a line segment joining the points (3,-2) and (15,3) .

An engineer is in the process of constructing two straight roads, RI and R, which will meet at the right angles. If RI will be represented by the equation 2x—3y—4=0 and R, will pass through the point , find the equation representing R2 in the form ax+by+c=0

OBCA form a quadrilateral with coordinates A (-5, 0), B(4,3) C(-1,3) and O(0,0)

1. Find the slopes of the line segments 
2. AO and CB     (ii) AC and OB
3. Find the distance AO, CB, AC and OB
4. Find the equation of the lines AB and CO and show that they are perpendicular. Using name (a), (b) and (c) suggest the name of the quadrilateral OBCA

(a) The coordinate of P, Q and R are (2, m), (-3, 1) and (6, n) respectively. If the length of PQ is  units and midpoint of QR is  find the possible value of m and n

(b)The gradient of line is -2. Another line L₂ is perpendicular to L₁ and passes through (-3,-2). What is the equation of L₂

The gradient of line L₁is -2. Another line L₂ is perpendicular to L₁ and passes through point (-3, -2). What is the equation of L₂?

The distance between (1,5) and (k+5, k+1) is 8. Find K, given that it is positive

Find the equation of the line passing through (6,4) and perpendicular to the line whose equation is 12x + 6y = 9.

Find the equation of the line through the points (4,6) and the midpoint of (2,4) and (10,4).

Find the distance between point (? 3,? 2) and the point midway between (2,13) and (4,7). Write your answer in the form a?c where a and c are positive real numbers.

If a line passing through the point (4, 2) is perpendicular to another line whose equation is 2x + 3y + 14 = 0, find the equation of the line.