Question

The midpoint of (-5,12) and (9,-2) divides the join of the points (-8,-5), (7,10) in the ratio???? ​

Answer 1

Answer:

2:1

Step-by-step explanation:

We know that mid-point formula of two points (x1,y1) and (x2,y2)

$x = \frac{x_1 + x_2}{2} \\ \\ y = \frac{y_1 + y_2}{2}$

1) Finding the midpoint of (-5,12) and (9,-2)

$x = \frac{ - 5 + 9}{2} \\ \\ = 2 \\ \\ y = \frac{12 + 2}{2} = 7$

Midpoint (2,7)

To find divides the join of the points (-8,-5), (7,10) in the ratio.

let the point (2,7) divides the line in k:1

From section formula

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

$2 = \frac{7k - 8}{k + 1} \\ \\ 2k + 2 = 7k - 8 \\ \\ 2k - 7k = - 8 - 2 \\ \\ - 5k = - 10 \\ \\ 5k = 10 \\ \\ \frac{k}{1} = \frac{2}{1}$

Hence the line is divided by 2:1

Hope it helps you.

Answer 2

Step-by-step explanation:

refers to the attachment