Question

Determine the ratio in which the point (6,

a.divides the line segment joining points a(9,-4) and b(2, 5). also, find the value of

a.

Answer 1

sorry I couldn't find the value of a.

Answer 2

Given:

A point (6,a) divides the line segment joining points a(9,-4) and b(2,5).

To find :

Ratio in which the point (6,a) divides the line segment joining points a(9,-4) and b(2,5) and value of a.

Solution:

Let point (6,a) divides the line segment joining points a(9,-4) and b(2,5) in the ratio k:1.

Section formula:

$x=\frac{m_1x_2+m_2x_1}{m_1+m_2},y=\frac{m_1y_2+m_2y_1}{m_1+m_2}$

Using the formula

$6=\frac{k(2)+1(9)}{k+1}$

$6k+6=2k+9$

$6k-2k=9-6$

$4k=3$

$k=\frac{3}{4}$

Ration: 3:4

$m_1=3,m_2=4$

Again using the formula for y

$a=\frac{3(5)+4(-4)}{3+4}$

$a=\frac{15-16}{7}$

$a=-\frac{1}{7}$