Prove that the point P dividing the line segment joining the points A( -1, 7 ) and B( 4, -3 ) in the ratio 3:2 , lies…
CBSE Class 10 Maths PYQ · Coordinate Geometry · Section Formula · 3 Marks · March 2026 · Standard
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1133 Marks · March 2026 · Standard
Prove that the point P dividing the line segment joining the points A($-1, 7$) and B($4, -3$) in the ratio $3:2$, lies on the line $x - 3y = -1$. Also find length of PA and PB.
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AP: PB = $3:2$ Coordinates of P = $(\frac{3\times 4+2\times (-1)}{3+2}, \frac{3\times (-3)+2\times 7}{3+2}) = (2,1)$ (1 Mark) Substituting $x = 2$ and $y = 1$ in the given equation L. H. S. = $x - 3y$ = $2 - 3(1)$ = $-1$ = R. H. S. $\therefore$ P lies on the given line (1 Mark) PA = $\sqrt{(2 + 1)^2 + (1 - 7)^2} = \sqrt{45}$ or $3\sqrt{5}$ (1/2 Mark) PB = $\sqrt{(2 - 4)^2 + (1 + 3)^2} = \sqrt{20}$ or $2\sqrt{5}$ (1/2 Mark)
