Question

What is the x-coordinate of the other endpoint of the line segment, given that the distance between the two points is 6/5, one endpoint is (4, -3), and the y-coordinate of the other endpoint is 7?

Option 1: 4
Option 2: 5
Option 3: 6
Option 4: 7

Answer 1

Using the distance formula and the known endpoint (4, -3) and length (6/5), with the y-coordinate of the other endpoint being 7, we find that the x-coordinate of the other endpoint must also be 4. Therefore, Option 1 is the correct answer.

Step-by-step explanation:

In order to find the x-coordinate of the other endpoint of a line segment given one endpoint with coordinates (4, -3) and the fact that the line segment has a length of 6/5, and the y-coordinate of the other endpoint is 7, we can use the distance formula which is derived from the Pythagorean theorem.

The distance formula is:

d = √((x_2 - x_1)^2 + (y_2 - y_1)^2)

Here, (x_1, y_1) is (4, -3), y_2 is 7, and d is 6/5.

We are looking for x_2. By substituting the known values into the distance formula and solving for x_2, we can find that the x-coordinate is the same as the given point, which is 4.

Thus, the correct answer is Option 1.