Question

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

A) 34
B) 16
C) 10
D) -6

Answer 1

To find the value of y, we need to determine the coordinates of the second line segment's endpoint. Since the given line segments are parallel, they have the same slope. Using the slope, we can find the equation of the line and solve for y. The value of y is 16.

Step-by-step explanation:

To find the value of y, we need to determine the coordinates of the second line segment's endpoint. Since the given line segments are parallel, they have the same slope. We can find the slope of the first line segment using the formula:

slope = (change in y) / (change in x)

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

The second line segment is parallel to the first, so it will also have a slope of -6. Using this slope and one of the points on the second line segment, we can find the equation of the line and solve for y.

y - 4 = -6(x - 5)

y - 4 = -6x + 30

y = -6x + 34

Since the second endpoint of the line segment has coordinates (3, y), we can substitute x = 3 into the equation:

y = -6(3) + 34 = -18 + 34 = 16

Therefore, the value of y is 16.