First slide

Equation of line in Straight lines

Question

A straight line through the origin O meets the parallel lines 4x + 2y = 9 and2x + y + 6 = 0 at points P and Q respectively. Then the point O divides the segment PQ in the ratio

Easy

A

1:2
B

3:4
C

2:1
D

4 : 3

Solution

Let any line through the origin meets the given lines at E and F as shown in figure.
Now, from the figure, triangles OAE and OCF are similar. Therefore,
$\frac{O E}{O F} = \frac{O A}{O C} = \frac{9 / 4}{3} = \frac{3}{4}$

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