QQuestion
Use the following graph and answer the given questions :
(a) Write the co-ordinates of points A, B and C.
(b) Find the equation of a line passing through the mid-point of AC and parallel to AB.
ICSEClass XMathematicsEquation Of Straight Line03 Mark2026 Easy
✓Answer
(a) From the graph:
A(4, 8), B(−1, 2) and C(6, 2).
(b) Mid-point of AC = \left(\frac{4+6}{2},\frac{8+2}{2}\right)
⇒ Mid-point of AC = (5, 5)
Slope of AB = \frac{8-2}{4-(-1)}
⇒ Slope of AB = \frac{6}{5}
The required line is parallel to AB, so its slope is also 6/5.
Using the point-slope form through (5, 5):
y − 5 = \frac{6}{5}(x − 5)
⇒ 5(y − 5) = 6(x − 5)
⇒ 5y − 25 = 6x − 30
⇒ 6x − 5y − 5 = 0
Therefore, the required equation is 6x − 5y − 5 = 0.
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