Question

Find the ratio in which the x-axis divides the line segment joining the points (−6, 5) and (−4, −1), Also, find the point of intersection.

Answer 1

Let the points be (−6, 5) and (−4, −1).

Let point P be the required point.

Now, we have to find the ratio.

Let the ratio be k : 1.

Hence, 

m₁ = k, m₂ = 1

x₁ = −6, y₁ = 5

x₂ = −4, y₂ = −1

y = 0, Finding the y coordinate using the section formula.

y = `(m_1  y_2 + m_2  y_1)/(m_1 + m_2)`

0 = `(k(-1) + 1(5))/(k + 1)`

0 = `(-k + 5)/(k + 1)`

0(k + 1) = (−k + 5)

0 = −k + 5

k = 5

Hence, k = 5

Now, use the same ratio (k = 5) to find the x-coordinate.

x = `(m_1  x_2 + m_2  x_1)/(m_1 + m_2)`

= `(k(-4) + 1(-6))/(k+1)`

= `(5(-4) + 1(-6))/(5+1)`

= `(-20-6)/6`

= `(-26)/6`

= `(-13)/3`

Hence the coordinate of point is P(x, y) = P `((-13)/3, 0)`.