Reflect a Figure in a Line
Draw the reflected image of quadrilateral WXYZ in
line p.
Step 1 Draw segments
perpendicular to line p from
each point W, X, Y, and Z.
Step 2 Locate W', X', Y',
and Z' so that line p is the
perpendicular bisector of
Points W', X', Y', and Z' are
the respective images of W,
X, Y, and Z.
Reflect a Figure in a Line
Step 3 Connect vertices
W', X', Y', and Z'.
Answer: Since points W',
X', Y', and Z' are the images
of points W, X, Y, and Z
under reflection in line p, then
quadrilateral W'X'Y'Z' is the
reflection of quadrilateral
WXYZ in line p.
Draw the reflected image of quadrilateral ABCD in
line n.
A.
B.
C.
D.
A.
B.
C.
D.
A
B
C
D
Minimize Distance by Using a
Reflection
BILLIARDS Suppose that you must bounce the cue
ball off side A before it rolls into the pocket at B.
Locate the point C along side A that the ball must
hit to ensure that it will roll directly toward the
pocket.
Minimize Distance by Using a
Reflection
Understand
You are asked to locate a point C on
side A such that the cue ball will bounce
off to roll into the pocket at point B.
Plan
For the cue ball to roll into the pocket at
B, it must hit point C on side A
somewhere in between where it sits
now and the pocket at B. Use the
reflection of point B on the continuation
of the line that B lies on to help find this
point.
Minimize Distance by Using a
Reflection
Solve
Draw point such that the corner pocket
is the midpoint between B and B'.
Connect the cue ball with B' using a line. Locate point C
at the intersection of the line drawn and side A.
Minimize Distance by Using a
Reflection
Answer:
Check
Check that BC  B'C so that ΔBCB' is an
isosceles triangle.
MINIATURE GOLF Omar is playing
miniature golf at a local course. Because
a wall is blocking his direct shot, he
needs to bounce the ball off wall W and
hit the hole located at point H. Which of
these steps would be needed to
determine where on wall W Omar should
aim?
A. Determine how far the obstructing wall is
from the ball.
B.
Reflect point H over the line formed by wall
W.
C.
Determine the exact length of wall W.
D.
Find the perpendicular distance from the
hole to the wall.
A.
B.
C.
D.
A
B
C
D
Reflect a Figure in a Horizontal or Vertical Line
A. Quadrilateral JKLM has vertices J(2, 3), K(3, 2),
L(2, –1), and M(0, 1). Graph JKLM and its image
over x = 1.
Reflect a Figure in a Horizontal or Vertical Line
Use the horizontal grid lines to find a corresponding point
for each vertex so that each vertex and its image are
equidistant from the line x = 1.
Answer:
Reflect a Figure in a Horizontal or Vertical Line
B. Quadrilateral JKLM has vertices J(2, 3), K(3, 2),
L(2, –1), and M(0, 1). Graph JKLM and its image
over y = –2.
Reflect a Figure in a Horizontal or Vertical Line
Use the vertical grid lines to find a corresponding point
for each vertex so that each vertex and its image are
equidistant from the line y = –2.
Answer:
A. Quadrilateral ABCD has vertices A(1, 2), B(0, 1),
C(1, –2), and D(3, 0). Graph ABCD and its image
over x = 2.
A.
C.
B.
D.
A.
B.
C.
D.
A
B
C
D
B. Quadrilateral WXYZ has vertices W(2, 4), X(3, 3),
Y(2, 0), and Z(0, 2). Graph WXYZ and its image over
y = –1.
A.
C.
B.
D.
A.
B.
C.
D.
A
B
C
D
Reflecting over the x- or y-axis
Reflect a Figure in the x- or y-axis
A. Graph quadrilateral ABCD
with vertices A(1, 1), B(3, 2),
C(4, 1), and D(2, 3) and its
image reflected in the x-axis.
Multiply the y-coordinate of each
vertex by –1.
(x, y)
→
(x, –y)
A(1, 1)
B(3, 2)
C(4, –1)
D(2, –3)
→
→
→
→
A'(1, –1)
B'(3, –2)
C'(4, 1)
D'(2, 3)
Reflect a Figure in the x- or y-axis
Answer:
Reflect a Figure in the x- or y-axis
B. Graph quadrilateral ABCD
with vertices A(1, 1), B(3, 2),
C(4, 1), and D(2, 3) and its
reflected image in the y-axis.
Multiply the x-coordinate of each
vertex by –1.
(x, y)
→
(–x, y)
A(1, 1)
B(3, 2)
C(4, –1)
D(2, –3)
→
→
→
→
A'(–1, 1)
B'(–3, 2)
C'(–4, –1)
D'(–2, –3)
Reflect a Figure in the x- or y-axis
Answer:
A. Graph quadrilateral LMNO with vertices L(3, 1),
M(5, 2), N(6, –1), and O(4, –3) and its reflected
image in the x-axis. Select the correct coordinates
for the new quadrilateral L'M'N'O'.
A. L'(3, –1), M'(5, –2),
N'(6, 1), O'(4, 3)
B. L'(–3, 1), M'(–5, 2),
N'(–6, –1), O'(–4, –3)
C. L'(–3, –1), M'(–5, –2),
N'(–6, 1), O'(–4, 3)
D. L'(1, 3), M'(2, 5),
N'(–1, 6), O'(–3, 4)
A.
B.
C.
D.
A
B
C
D
B. Graph quadrilateral LMNO with vertices L(–1, 0),
M(1, 1), N(2, –2), and O(0, –4) and its reflected image
under the y-axis. Select the correct coordinates for
the point M' in the new quadrilateral L'M'N'O'.
A. L'(–1, 0), M'(1, –1),
N'(2, 2), O'(0, 4)
B. L'(1, 0), M'(–1, 1),
N'(–2, –2), O'(0, –4)
C. L'(1, 0), M'(–1, –1),
N'(–2, 2), O'(0, 4)
D. L'(0, –1), M'(1, 1),
N'(–2, 2), O'(–4, 0)
A.
B.
C.
D.
A
B
C
D
Reflecting over the line y = x
Reflect a Figure in the Line y = x
Quadrilateral ABCD with vertices
A(1, 1), B(3, 2), C(4, 1), and
D(2, 3). Graph ABCD and its
image under reflection of the line
y = x.
Interchange the x- and y-coordinates
of each vertex.
(x, y)
→
(y, x)
A(1, 1)
B(3, 2)
C(4, –1)
D(2, –3)
→
→
→
→
A'(1, 1)
B'(2, 3)
C'(–1, 4)
D'(–3, 2)
Reflect a Figure in the Line y = x
Answer:
Quadrilateral EFGH has vertices E(–3, 1), F(–1, 3),
G(1, 2), and H(–3, –1). Graph EFGH and its image
under reflection of the line y = x. Select the correct
coordinates for the point H' in the new quadrilateral
E'F'G'H'.
A. E'(–3, –1), F'(–1, –3),
G'(1, –2), H'(–3, 1)
B. E'(3, –1), F'(1, –3),
G'(–1, 2), H'(3, –1)
C. E'(1, –3), F'(3, –1),
G'(2, 1), H'(–1, –3)
D. E'(–1, 3), F'(–3, 1),
G'(–2, –1), H'(1, 3)
A.
B.
C.
D.
A
B
C
D