Question

Point A(-4,1) is in the standard (x,y) coordinate plane. What must be the coordinates of point B so that the line x=2 is the perpendicular bisector of bar (AB) ?

Answer 1

Point B must have coordinates (8,1) so that the line x=2 is the perpendicular bisector of the line segment AB where A has coordinates (-4,1).

Step-by-step explanation:

To find the coordinates of point B such that the line x=2 is the perpendicular bisector of the segment AB, with A given as (-4, 1), we follow a specific strategy.

Step 1: Identify the mid-point formula for a line segment (Mx, My) = ((x1 + x2)/2, (y1 + y2)/2). Since x=2 is the perpendicular bisector, Mx must equal 2.

Step 2: Calculate the mid-point Mx using the x-coordinate of A: Mx = (x1 + x2)/2 = (2 + (-4))/2 = (-2)/2 = -1. Since the bisector x=2, we solve for x2: 2 = (x1 + x2)/2, hence x2 = 2*2 - x1 = 4 - (-4) = 8.

Step 3: The y-coordinate of B (y2) will be the same as A (y1), which is 1, as the y-coordinate does not affect the x-position of the midpoint when the bisector is vertical.

Therefore, the coordinates of point B will be (8, 1).