given the point A(-2,3).Find the coordinates of point B, such that the line x=4 is a perpendicular bisector of the line AB

To find the coordinates of point B such that the line x = 4 is a perpendicular bisector of line AB, we need to first understand the properties of a perpendicular bisector.

First, let's analyze the equation x = 4. This equation represents a vertical line passing through the point (4, 0) on the x-axis. Since the x-coordinate is constant, the slope of this line is undefined (or infinite).

For line AB to be perpendicular to x = 4, its slope should be the negative reciprocal of the slope of the line x = 4. Let's determine the slope of line AB.

The slope of a line passing through two points (x1, y1) and (x2, y2) can be calculated using the formula:

slope = (y2 - y1) / (x2 - x1)

Given point A (-2, 3) and point B (x, y), we can use these values to calculate the slope of line AB.

slope_AB = (y - 3) / (x - (-2))

Next, we need to calculate the slope of the line that is perpendicular to x = 4.

The negative reciprocal of the slope of the line x = 4 will be the slope of the line AB. Since the slope of x = 4 is undefined (or infinite), the negative reciprocal will be 0.

slope_AB = 0

To find the coordinates of point B, we need to find a point where the line AB has a slope of 0, which means it is a horizontal line. A horizontal line has a constant y-coordinate.

Since point A is (-2, 3), the y-coordinate will remain the same for point B.

Therefore, the coordinates of point B, such that the line x = 4 is a perpendicular bisector of the line AB, are (4, 3).