Coordinate Geometry Question - CBSE

Question

If $A(3, 2)$ and $B(-1, 8)$ are two given points, find the coordinates of the point $P$ on the line segment $AB$ such that $AP = \dfrac{3}{4} AB$. Using coordinate geometry, verify that $P$ divides $AB$ in the ratio $3 : 1$.

Accepted Answer

$AP = \dfrac{3}{4} AB \Rightarrow PB = AB - AP = \dfrac{1}{4} AB \Rightarrow AP : PB = 3 : 1$. [1.5 Marks]
$x = \dfrac{3(-1) + 1(3)}{3 + 1} = \dfrac{-3 + 3}{4} = 0$. [1.5 Marks]
$y = \dfrac{3(8) + 1(2)}{3 + 1} = \dfrac{24 + 2}{4} = \dfrac{26}{4} = \dfrac{13}{2}$. Point $P$ is $\left(0, \dfrac{13}{2}\right)$. [2.0 Marks]

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🎯 Official CBSE Marking Scheme:
Deducing ratio $AP : PB = 3 : 1$: 1.5 Marks
Calculating $x_P = 0$: 1.5 Marks
Calculating $y_P = 13/2 \Rightarrow P(0, 13/2)$: 2.0 Marks

Question:

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