Mathematics
A and B are the two points on the x-axis and y-axis respectively. P(2, -3) is the mid-point of AB.
Find :
(i) the coordinates of A and B.
(ii) the slope of the line AB.
(iii) the equation of the line AB.
Straight Line Eq
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Answer
(i) Let the coordinates of A be (x, 0) and B be (0, y).
P(2, -3) is the mid-point of AB. So we have,
Hence. the coordinates of A are (4, 0) and B are (0, -6).
(ii) Slope of AB =
Putting values we get slope,
Hence, the slope of the line AB is
(iii) Equation of AB will be
⇒ y - y1 = m(x - x1)
⇒ y - 0 = (x - 4)
⇒ 2y = 3x - 12
⇒ 3x - 2y = 12.
Hence, the equation of AB is 3x - 2y = 12.
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