NumericalModerate1.5 marks
9(b)
A(-1, 3), B(4, 2) and C(3, -2) are the vertices of a triangle.
Find the equation of the line through G and parallel to AC
Topic: Slope / equation of line
Previous-year question practice database
Answer
Exam answer
A(−1, 3) C(3, −2) G(2, 1)
Slope of AC:
mAC = (−2 − 3)/(3 − (−1))
= −5/4
The required line through G is parallel to AC.
Therefore its slope is also −5/4.
Using point-slope form through G(2,1):
y − 1 = (−5/4)(x − 2)
4y − 4 = −5x + 10
5x + 4y − 14 = 0
Answer:
5x + 4y − 14 = 0.
Explanation
Parallel lines have equal slopes. Find the slope of AC first, then use the point-slope equation for the line through the centroid G.
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