Question

In what ratio the line segment joining the points A(1,1) and B(-1,3) is divided by the y-axis?

Answer 1

In order to better understand, let's draw the segment and both axis:

Then, let's calculate the slope of this segment, using the following formula for two points (x1, y1) and (x2, y2):

$m=\frac{y_2-y_1}{x_2-x_1}$

Using points A and B, we have:

$m=\frac{3-1}{-1-1}=\frac{2}{-2}=-1$

That means for every unitary increase in x, the value of y decreases by 1 unit.

So, from point (-1, 3), let's add 1 unit to x and decrease 1 unit from y, then we have point (0, 2).

We can see that both x and y coordinates of this new point are the average of A and B coordinates (0 is the average of -1 and 1, 2 is the average of 1 and 3).

Therefore the line segment AB is divided in a ratio of 1 to 1 (it is divided into two equal segments)