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Question
A straight line passes through the points P(–1, 4) and Q(5, –2). It intersects the co-ordinate axes at points A and B. M is the mid-point of the segment AB. Find:
- The equation of the line.
- The co-ordinates of A and B.
- The co-ordinates of M.
Solution
i. Slope of PQ =`(-2 - 4)/(5 + 1) = (-6)/6 = -1`
Equation of the line PQ is given by
y – y1 = m(x – x1)
y − 4 = −1(x + 1)
y − 4 = −x − 1
x + y = 4 − 1
x + y = 3
ii. For point A (on x-axis), y = 0.
Putting y = 0 in the equation of PQ, we get,
x = 3
Thus, the co-ordinates of point A are (3, 0).
For point B (on y-axis), x = 0.
Putting x = 0 in the equation of PQ, we get,
y = 3
Thus, the co-ordinates of point B are (0, 3).
iii. M is the mid-point of AB.
So, the co-ordinates of point M are
`( (3 + 0)/2 , (0 + 3)/2) = (3/2, 3/2)`
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