The image of point A(-2, 5) is point A’(1, -2) after a reflection over line
k. The equation for line k is in the form y = mx + b. What is the value of m?
the axis of reflection is perpendicular to the line joining the two points.
So, use the usual way to find the slope of that line segment, and then take its negative reciprocal.
Two lines with slopes m1 and m2 are perpendicular if m1 * m2 = -1
Thank you sir !!
To determine the value of m, which represents the slope of line k, we can use the fact that the image of point A is A' after reflection over line k.
Given that A(-2, 5) reflects to A'(1, -2), we can calculate the slope of the line passing through these two points.
Recall that the slope of a line passing through two points (x₁, y₁) and (x₂, y₂) can be calculated using the formula m = (y₂ - y₁) / (x₂ - x₁).
Using this formula, we can determine the slope of line k by substituting the coordinates of A and A':
m = (-2 - 5) / (1 - (-2))
= (-7) / (1 + 2)
= -7 / 3
Therefore, the value of m, representing the slope of line k, is -7/3.