Question

Calculate the ratio in which the line segment joining the points $A(6, 5)$ and $B(4, -3)$ is divided by the line $y = 2$. Also, find the point of intersection.

Accepted Answer

Let the ratio be $k : 1$. $y$-coordinate of division point = $\frac{-3k + 5}{k + 1} = 2 \implies -3k + 5 = 2k + 2 \implies 5k = 3 \implies k = \frac{3}{5}$. Ratio is $3 : 5$. $x$-coordinate = $\frac{3(4) + 5(6)}{3 + 5} = \frac{12 + 30}{8} = \frac{42}{8} = \frac{21}{4}$. Point of intersection is $\left(\frac{21}{4}, 2\right)$.

Section formula with line y = 2

Explanation

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