First slide

Cartesian plane

Question

The points whose co–ordinates are $x = x_{1} + t (x_{2} - x_{1}), y = y_{1} + t (y_{2} - y_{1})$ divides the join of $(x_{1}, y_{1})$ and $(x_{2}, y_{2})$ in the ratio

Moderate

A

$\frac{t}{1 + t}$
B

$\frac{1 + t}{t}$
C

$\frac{t}{1 - t}$
D

$\frac{1 - t}{t}$

Solution

$x = x_{1} + t (x_{2} - x_{1}), y = y + t (y_{2} - y_{1})$
$x = \frac{(1 - t) x_{1} + t x_{2}}{(1 - t) + t}, y = \frac{(1 - t) + t y_{2}}{(1 - t) + t}$

$\Rightarrow$ $p (x, y)$ divides join of $A (x_{1}, y_{1})$ & $B (x_{2}, y_{2})$ in the ratio $t : 1 - t$

Ratio $= \frac{t}{1 - t}$

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