Question

Let P be the point of intersection of the lines $3x + 4y = 2a$ and $7x + 2y = 2018$ and Q the point of intersection of the lines $3x + 4y = 2018$ and $5x + 3y = 1$

If the line through P and Q has slope 2, the value of a is:

Accepted Answer

C. Solving for Q from $3x + 4y = 2018$ and $5x + 3y = 1$ gives $Q(-550, 917)$. P satisfies $3x + 4y = 2a$ and $7x + 2y = 2018$. Subtracting gives $4x - 2y = 2018 - 2a \Rightarrow y - 2x = a - 1009$. Since line PQ has slope 2, $y - 2x$ is constant for all points on PQ. For Q(-550, 917): $y_Q - 2x_Q = 917 - 2(-550) = 2017$. Thus $a - 1009 = 2017 \Rightarrow a = 3026$.

Coordinate Geometry: Line Intersections and Slope

Explanation

Practise this under exam conditions