Question

Two line segments are parallel to each other. The first line segment has end points at (2,3) and (1,9). The second line segment has end points at (5,4) and (3,y). What is the value of y?

Answer 1

To ensure the line segments are parallel, their slopes must be the same. The slope of the first segment is -6, and setting the slope of the second segment equal to this, we solve for y to find that y = 16.

Step-by-step explanation:

To find the value of y for the second line segment, we need to ensure it is parallel to the first line segment. Parallel lines have the same slope. The slope of the first line segment can be calculated using its end points (2,3) and (1,9). The slope is the change in y over the change in x, thus:

Slope = (9 - 3) / (1 - 2) = 6 / -1 = -6

Now, we must find the slope of the second line segment using its end points (5,4) and (3,y). As the slopes must be equal for the lines to be parallel:

Slope = (y - 4) / (3 - 5)

Setting this slope equal to the slope of the first line (-6), we get:

-6 = (y - 4) / (3 - 5)

Multiply both sides by -2 to clear the fraction:

12 = y - 4

Add 4 to both sides to solve for y:

y = 16

Therefore, the value of y for the second line segment to ensure it is parallel to the first is 16.