Questions: (-6,-2) ratio 1:4 S(5,6)

Transcript text: $(-6,-2)$ ratio 1:4 S(5,6)

Solution

Solution Steps

To find the point that divides the line segment joining the points $(-6, -2)$ and $S(5, 6)$ in the ratio 1:4, we can use the section formula. The section formula for a point dividing a line segment in the ratio $m:n$ is given by: \[ \left( \frac{mx_2 + nx_1}{m+n}, \frac{my_2 + ny_1}{m+n} \right) \]

Solution Approach

Identify the coordinates of the points and the ratio.
Apply the section formula to find the coordinates of the dividing point.

Step 1: Identify the Coordinates and Ratio

Given points are $(-6, -2)$ and $ (5, 6) $. The ratio is $1:4$.

Step 2: Apply the Section Formula

The section formula for a point dividing a line segment in the ratio $m:n$ is: \[ \left( \frac{mx_2 + nx_1}{m+n}, \frac{my_2 + ny_1}{m+n} \right) \] Substituting the given values: \[ x = \frac{1 \cdot 5 + 4 \cdot (-6)}{1 + 4} = \frac{5 - 24}{5} = \frac{-19}{5} = -3.8 \] \[ y = \frac{1 \cdot 6 + 4 \cdot (-2)}{1 + 4} = \frac{6 - 8}{5} = \frac{-2}{5} = -0.4 \]