Question

Find the ratio in which the line segment joining (2,−3) and (5,6) is divided by the x-axis.

A) 2:5
B) 3:1
C) 1:2
D) 5:2

Answer 1

The ratio in which the line segment joining the points (2, -3) and (5, 6) is divided by the x-axis is 3:1. This is found by comparing the y-coordinates of the given points with respect to the y-coordinate of the x-axis (which is 0).

Step-by-step explanation:

To find the ratio in which the line segment joining the points (2, -3) and (5, 6) is divided by the x-axis, we need to calculate the point where the line segment intersects the x-axis. This point will have a y-coordinate of 0, since it lies on the x-axis. We can use the two-point form of the line equation or the section formula to find this ratio.

However, since we are specifically interested in the ratio, we can use a simpler method as follows:

Let the point where the line crosses the x-axis be (x, 0). Then, by considering the proportion of the y-coordinates, we can set up the following:

Ratio = (0 - (-3))/(6 - (-3)) = 3/9 = 1/3

So, the line segment is divided in the ratio 1:3 (part on the side of (2, -3) to the part on the side of (5, 6)). Therefore, our answer is B) 3:1, which means the section of the line on the x-axis side of (2, -3) is three times longer than the section on the other side of the x-axis.