Question

If the point C ( -1, 2) divides internally the line segment joining the points A (2, 5) and B (x , y) in the ratio 3 : 4, find the value of x2 - y 2 .

Answer 1

Answer:

$- 1 = \frac{3x + 4 \times 2}{3 + 4} = \frac{3x + 8}{7}$

$3x + 8 = - 7 \: \: so \: \: x = - \frac{15}{3} = - 5$

now,

$2 = \frac{3y + 4 \times 5}{3 + 4} = \frac{3y + 20}{7}$

$3y + 20 = 14 \: \: i.e \: y = \frac{ - 6}{3} = - 2$

i.e,

${x}^{2} - {y}^{2} = ( { - 5)}^{2} - {( - 2)}^{2} = 25 - 4 = 21 \: \: \: ans.$