Question

point A is located at (-4,8) on then coordinate plane. Point B is located at (4,8). point c is plotted on the horizontal line connecting point A and Point B. the distance between point c and point a is the same distance between point c and b!!What are the coordinates of point c!!

Answer 1

The coordinates of point C, the midpoint between points A (-4, 8) and B (4, 8), are (0, 8) as it is equidistant from both points A and B on the coordinate plane.

The coordinates of point C are (0, 8).

Step-by-step explanation:

To find the coordinates of point C on a coordinate plane where it is equidistant from points A (-4, 8) and B (4, 8), you must locate the midpoint of the line segment connecting these two points. Since points A and B have the same y-coordinate, point C will also have this y-coordinate (8). Because point A is at x = -4 and point B is at x = 4, and point C is exactly in between, the x-coordinate of point C must be halfway between -4 and 4. The midpoint on the x-axis between two points is calculated by adding the x-coordinates of both points and dividing by 2.

If we add the x-coordinates of points A and B: (-4) + (4) = 0.

Then, we divide by 2: 0 / 2 = 0.

Therefore, the x-coordinate for point C is 0.

Combining these results, the coordinates of point C are (0, 8).

Answer 2

The coordinates of the point C is (0,8)

Here, we want to get the coordiates of point C

From the question, it can be seen that point C is equidistant from points A and B

What this mean is that it is at the midpoint of AB

We can use the mid-point formula to get the coordinates of point B

We have this as;

`\begin{gathered} (x,y)\text{ = (}(x_2+x_1)/(2),(y_2+y_1)/(2)) \\ \\ (x_1,y_1)=\text{ (-4,8)} \\ (x_2,y_2)\text{ = (4,8)} \\ \\ (x,y)\text{ = (}(4-4)/(2),(8+8)/(2)) \\ \\ (x,y)\text{ = (0,8)} \end{gathered}`