Question

A point Q (X,Y) is on the line segment passing through R(-2, 5) and S (4,1). Find the coordinates of Q if it is twice as far from R as from S

Answer 1

Answer:

$\huge{\pink{\green{\sf{\therefore Q(0,\frac{11}{3})}}}}$

Step-by-step explanation:

$\huge{\pink{\green{\underline{\red{\sf{SOLUTION-}}}}}}$

▪In the given question information is given about a line segment whose two end points coordinates are given.

▪And one coordinate between these two ends divides this line the given ratio.

▪According to given question :

$\underline \bold{given : } \\ \implies\bold{coordinate \: of \: R( - 2,5)} \\ \implies \bold{coordinate \: of \: S( - 4.1)} \\ \implies \bold{m : n = 1 :2} \\ \\ \underline \bold{to \: find : } \\ \implies \bold{coordinate \: of \: Q( x,y)}$

▪According to the section formula(internal ratio).

$\implies x = \frac{mx_{2} + nx_{1} }{m + n} \\ \implies x = \frac{1 \times 4 + 2 \times ( - 2)}{1 + 2} \\ \implies x = \frac{4 - 4}{3} \\ \bold{\implies x = 0} \\ \\ \implies y = \frac{ my_{2} + ny_{1}}{m + n} \\ \implies y = \frac{1 \times 1 + 2 \times 5}{1 + 2} \\ \implies y = \frac{1 + 10}{ 3 } \\ \bold{\implies y = \frac{11}{3} }\\\\\bold{\therefore Q(0,\frac{11}{3})}$

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