Question

The line AB is parallel to the x-axis with point A(3, a), and the midpoint of AB is (5, 1). Calculate:

(a) the value of a.
a) 0
b) 2
c) 3
d) 4
(b) the coordinates of B.
a) (7, 1)
b) (9, 1)
c) (5, -1)
d) (5, 3)

Answer 1

The value of a is not in the options provided, but logically it should be 1. The coordinates of point B are determined to be (7, 1) using the midpoint formula.

Step-by-step explanation:

To solve for the value of a and the coordinates of point B, we rely on the properties of a midpoint in a line segment. Given that line AB is parallel to the x-axis and has a midpoint at (5, 1), we can assert that Point A has the same y-coordinate as Point B because the y-coordinate doesn't change when moving along a line parallel to the x-axis.

Since the midpoint's y-coordinate is 1, the y-coordinate for both A and B must also be 1. Hence, point A is at (3,1), not (3, a) as initially assumed. This means a is equal to 1, which is not listed in the options provided. However, assuming this was an oversight in the options, we have answered part (a).

For part (b), to find the coordinates of point B knowing that (5, 1) is the midpoint, we will apply the midpoint formula which states that the x-coordinate of the midpoint is the average of the x-coordinates of A and B. We then solve for the x-coordinate of B:

(3 + xB) / 2 = 5

Solving for xB gives us:

10 = 3 + xB
xB = 7

Therefore, the coordinates of point B are (7, 1),