Question

Find the ratio in which the point P(11, y) divides the line segment

Joining the points A(15,5) and B(9, 20). Also, find the value of y.​

Answer 1

ratio: 2:1

y = 15

Explanation:

The ratio would be 15-11:11-9 = 4:2 = 2:1

This is because you can subtract the x values of the two points with 11.

To find the value of y:

Figure out the equation of the line between the two points by putting it in the form y = mx + b where m is the slope and b is the y-intercept.

To find the slope, use change in y/change in x so:

20 - 5/9-15 = 15/-6 = 5/-2 = -2.5

That means the slope is -2.5, so you have:

y = -2.5x + b

since you know the point (15, 5) is a solution, you can plug x = 15 and y = 5 into the equation:

5 = -2.5 * 15 + b

5 = -37.5 + b

b = 42.5

The equation is: y = -2.5x + 42.5

Then, plug in x = 11 into the equation:

y = -2.5*11 + 42.5

y = -27.5 + 42.5

y = 15