1) Find the reflection of \(A(-9, 7)\) in the following lines:
a) \(y = x\)
b) \(y = -x\)
c) \(y = -2x\)
d) \(y = \Large\frac{5}{4}\normalsize x\)
2) Point \(Q' = (3, 7)\) is the image of a point after a reflection in \(y = -x + 4\). Find the pre-image \(Q\).
3) In a circle whose center is at \(P\), the image of \(A(4, 6)\) over \(P\) is \(A'(-2, -2)\). Find the image of \(B(-3, 5)\) over \(P\).
4) Find the image of \(B(-3, 2)\) reflected in
a) \(y = 3\) and then in \(y = -5\).
a) Describe a single transformation that maps \(B\) onto \(B''\) in (a).
a) \(y = x\)
b) \(y = -x\)
c) \(y = -2x\)
d) \(y = \Large\frac{5}{4}\normalsize x\)
2) Point \(Q' = (3, 7)\) is the image of a point after a reflection in \(y = -x + 4\). Find the pre-image \(Q\).
3) In a circle whose center is at \(P\), the image of \(A(4, 6)\) over \(P\) is \(A'(-2, -2)\). Find the image of \(B(-3, 5)\) over \(P\).
4) Find the image of \(B(-3, 2)\) reflected in
a) \(y = 3\) and then in \(y = -5\).
a) Describe a single transformation that maps \(B\) onto \(B''\) in (a).
5) Drag the blue point so that it shows the reflection of the red point across the purple line and then across the green line.
6) Find the coordinates of \(H\), if the path from \(S\) to \(H\) to \(O\) is the shortest distance from \(S\) to the \(y\)-axis to \(O\).
7) A golf ball is hit from \((4, 8)\) towards the \(y\) –axis, bounces off the \(y\)–axis, and lands at \((6, –13)\). Where on the \(y\)–axis did the ball bounce?
8) If \(H\) is reflected in the barrier at \(y = 10\) to \(H'\), find the slope of \(\overline{GH'}\). Where does \(\overline{GH'}\) intersect \(y = 10\)?
8) If \(H\) is reflected in the barrier at \(y = 10\) to \(H'\), find the slope of \(\overline{GH'}\). Where does \(\overline{GH'}\) intersect \(y = 10\)?
9) On the miniature-golf hole shown, the ball is at \(G(1, 1)\) and the hole is at \(H(6, 2)\). A player can make a hole in one by hitting the ball along the path indicated by the arrows. Find the coordinate of point \(A\), \(B\), and \(C\). Using Desmos may help.
10) On the miniature-golf hole shown, the ball is at \(G(6, 0)\) and the hole is at \(H(4, 2)\). Jeff wants the ball to strike the barrier at \(y = 8\), the barrier at \(x = 0\), and the barrier at \(y = -1\) before it goes into the hole.
a) Find the coordinates of \(A\), the point at which the ball should strike the first barrier.
b) Find the coordinates of \(B\), the point at which the ball should strike the second barrier.
c) Find the coordinates of \(C\), the point at which the ball should strike the third barrier.
a) Find the coordinates of \(A\), the point at which the ball should strike the first barrier.
b) Find the coordinates of \(B\), the point at which the ball should strike the second barrier.
c) Find the coordinates of \(C\), the point at which the ball should strike the third barrier.
11) Using a set of reflections, find a hole-in-one path from \(G\) to \(H\)
12) The line \(y = 3x + 2\) is reflected in the line \(y = -1\). What is the equation of the image?
13) Point \(B’(1, 4)\) is the image of \(B(3, 2)\) after a reflection in line \(c\). Write an equation of line \(c\).
14) Given the points \(A(3, 2), B(6, 14),\) and \(C(5, 20)\). If \(\triangle ABC\) is reflected over the \(y\)–axis, then find the new coordinates of this triangle.
15) Find the equation of the line when the graph \(y =\Large\frac{7}{2}\normalsize x + 3\) is reflected over the
line \(x = 6\).
16) Find the equation of the reflection of the line with equation \(3y – 2x – 2 = 0\) over the \(y\)-axis. Write in slope-intercept form.
17) The reflection across the line \(y = x\) maps \(P(2, 9)\) to \(P’\). Find the distance \(PP'\).
18) The line \(y = 3x + 7\) is reflected across the line \(y = x\) to create a second line. Find the slope of the second line.
19) The line \(y = \Large\frac{1}{2}\normalsize x – 4\) is reflected in the line \(x = 2\). What is the equation of the image?
13) Point \(B’(1, 4)\) is the image of \(B(3, 2)\) after a reflection in line \(c\). Write an equation of line \(c\).
14) Given the points \(A(3, 2), B(6, 14),\) and \(C(5, 20)\). If \(\triangle ABC\) is reflected over the \(y\)–axis, then find the new coordinates of this triangle.
15) Find the equation of the line when the graph \(y =\Large\frac{7}{2}\normalsize x + 3\) is reflected over the
line \(x = 6\).
16) Find the equation of the reflection of the line with equation \(3y – 2x – 2 = 0\) over the \(y\)-axis. Write in slope-intercept form.
17) The reflection across the line \(y = x\) maps \(P(2, 9)\) to \(P’\). Find the distance \(PP'\).
18) The line \(y = 3x + 7\) is reflected across the line \(y = x\) to create a second line. Find the slope of the second line.
19) The line \(y = \Large\frac{1}{2}\normalsize x – 4\) is reflected in the line \(x = 2\). What is the equation of the image?