NumericalEasy1 mark
8(c)
A line AB meets X – axis at A and Y –axis at B. P (4, -1) divides AB in the ratio 1 : 2.
Find the equation of the line through P and perpendicular to AB.
Topic: Slope / equation of line
Previous-year question practice database
Answer
Exam answer
From part (i):
A = (6, 0) B = (0, −3)
Slope of AB:
mAB = (−3 − 0)/(0 − 6)
= −3/−6
= 1/2
The required line is perpendicular to AB.
Therefore:
m × 1/2 = −1
m = −2
The line passes through P(4, −1).
Using point-slope form:
y − (−1) = −2(x − 4)
y + 1 = −2x + 8
2x + y − 7 = 0
Answer:
2x + y − 7 = 0.
Explanation
Use the coordinates found in part (i) to calculate the slope of AB. A perpendicular line has slope equal to the negative reciprocal, and the equation is then obtained through P(4, −1).
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