Geometry ive tried over and over cant seem to get it or understnad

Question

Point P'(-6,-4) is the image of point P(-2,3) after a translation. What is the image of point A(5,-1) after you apply the same translation?

Find the coordinates of the reflection without using the coordinate plane.

P (4,6) over the x-axis.

Find the coordinates of the reflection without using the coordinate plane.

Q (-3,5) over the y-axis.

A point A(-5,-3) is translated by the vector v = <8, 0>, and then reflected about the line y=0. the coordinates of its image A are _________.

Answer 1

To get to from (-2,3) to (-6,-4), this would require -4 units to the left and -8 units down. The translation would be <-4,-8>. If you apply the same translation to (5,-1), this would be (5-4,-1-8) simplified is (1,-9)

For reflections over the different axis, I find it helpful to plot the point rather than try to memorize the rules for applying the translations.

(4,6) is in the first quadrant. Reflecting on the x axis would but it into the 4th quadrant. The x coordinate is the same, the y has the opposite sign.

(4,6) over the x axis is (4,-6)

(-3,5) is in the second quadrant. Reflecting over the y axis would put in in the first quadrant. The x coordinate is the opposite sign, the y coordinate is the same.

(-3,5) over the y axis is (3,5)

(-5,-3) applying <8,0> is (-5+8,-3+0) which is (3,-3). The line y=0 is the x axis. Over the x axis for (3,-3) in the fourth quadrant would put the point in the first quadrant. The result would be (3,3)