Question

If P is a point lying on the line segment joining Q(1, 1) and R(4, 1) such that PQ = $\frac{3}{7}$QR , then find the coordinates of P .

Answer 1

Using the section formula, if a point $(x,y)$ divides the line joining the points $(x_1,y_1)$ and $(x_2,y_2)$ in the ratio $m:n$, then

$(x,y)=(\frac{m{x}_2+n{x}_1}{m+n},\frac{m{y}_2+n{y}_1}{m+n})$

Given-

$PQ=\frac{3}{7}QR$

Therefore,$PR=1-\frac{3}{7}$

$PR=\frac{4}{7}QR$

$PQ:PR=\frac{\frac{3}{7}}{\frac{4}{7}}$

$=3:4$

Therefore P dividesQR in ratio of $3:4$

$P=(\frac{3\times 4+4\times 1}{3+4},\frac{3\times 1+4\times 1}{3+4})$

$=(\frac{16}{7},1)$