Question

If the point C (-1,2) divides the line segment joining the points A(2,5) and B (x,y) in the ratio 3:4 internally. find the value of
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Answer 1

According to section formula, if P(x,y) divides the line through A(a,b) and B(c,d) in the ratio m:n

Then P is given by:

$P(x,y)= (\frac{mc+na}{mn},\frac{md+nd}{m+n})$

So,

$C(-1,2)=(\frac{3(x)+4(2)}{3+4},\frac{3(y)+4(5)}{4+4})$

$(-1,2)=(\frac{3x+8}{7} ,\frac{3y + 20}{7} )$

So,

$\frac{3x + 8}{7} = - 1 \: \mathtt{and} \: \frac{3y + 20}{7} = 2$

$x = - 5 \: \mathtt{and} \: y = - 2$

So,

${x}^{2} + {y}^{2} = ( - 5) {}^{2} + ( - 2) {}^{2} \\ = 25 + 4 \\ = { \boxed{ \red{29}}}$