Question

If the ratio in which the line segment joining the points (6,4) and (x,-7) divided internally by y-axis is 6:1, then x equals?

Answer 1

COORDINATE GEOMETRY :

Given, Ratio = 6 : 1

Coordinates for y- axis = ( 0,y )

$\textsf{m} _{1}$ = 6, $\textsf{m} _{2}$ = 1

$\textsf {x} _{1}$ = 6, $\textsf {x} _{2}$ = x

$\textsf {y} _{1}$ = 4, $\textsf {y} _{2}$ = - 7

Now, Using the Section - Formula,

x = $\mathsf{\frac{m_1 x_2 + m_2 x_1}{m_1 + m_2}}$

x = $\mathsf{\frac{6x + 6 }{6 + 1}}$

0 = $\mathsf{\frac{6x + 6 }{7}}$

0 = 6x + 6

6x = - 6

$\fbox{\textsf{x = - 1}}$

➡️ ANSWER : x = - 1