Question

a straight line passes through points P( - 1,4 )and Q( 5, - 2). It intersects x axis and y axis at points A and B respectively and M is the midpoint of AB.
find: 1..the equation of the line 2... the coordinates of A and B and 3....the coordinates of M

Answer 1

We have, P (– 1, 4) and Q (5, – 2) and line passes through P and Q.

Therefore, slope of the line = (y2 – y1)/(x2 – x1) = [– 2 – 4]/[5 – (– 1)] = – 6/6 = – 1.

(i) Thus the equation of the line is : y – y1 = m (x – x1)
Or,     y – 4  = (– 1) [x – (– 1)]
Or,      y – 4 = – x – 1
Or, x + y – 3 = 0

(ii) Putting y = 0, co-ordinates of A are (3, 0) and putting x = 0, co-ordinates of B are (0, 3).

(iii) Co-ordinates of ‘M’, mid-point of AB = [(x1 + x2)/2, (y1 + y2)/2]
= [(3 + 0)/2, (0 + 3)/2]
= (3/2, 3/2)

Answer 2

Here is your answer attached with paper

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