Reflect over any line and rotate about a point, with coordinate rules
Grade 10 Math Worksheet - Building Confidence

Circle the best answer, or write your answer on the line.
each square one unit, origin in the middle. Triangle QSU on Esme's castle design has corners Q(1, -4), S(5, 2) and U(-1, 6). It flips across the line x = -3. Where is Q′? Write it like (7, -3).
Triangle CDF on Jun's map design has corners C(-5, 1), D(2, 3) and F(0, -2). It flips across the line y = 4. Where is C′? Write it like (7, -3).
Coordinate grid, all four quadrants, each square one unit, origin in the middle. Triangle CDF is drawn with its corners labeled and the mirror line y = 4 drawn dashed across the grid; the image is not drawn. Coordinate grid, all four quadrants, each square one unit, origin in the middle. Triangle CDF is drawn with its corners labeled and the mirror line y = 4 drawn dashed across the grid; the image is not drawn. x y 0 C D F y = 4 Triangle CDF on Kira's crown design has corners C(1, 3), D(-4, 6) and F(2, -5). It flips across the line y = x. Where is D′? Write it like (7, -3).
Coordinate grid, all four quadrants, each square one unit, 20 squares across (−10 to 10), origin in the middle. Triangle CDF is drawn with its corners labeled and the line y = x dashed; the image is not drawn. Coordinate grid, all four quadrants, each square one unit, 20 squares across (−10 to 10), origin in the middle. Triangle CDF is drawn with its corners labeled and the line y = x dashed; the image is not drawn. −10 −8 −6 −4 −2 2 4 6 8 10 −10 −8 −6 −4 −2 2 4 6 8 10 0 y = x C D F A flip sends Pia's boat marker from P(-3, 6) to P′(5, 6). The mirror line is vertical (x = k). What is k?
Coordinate grid, all four quadrants, each square one unit, origin in the middle. Point P(-3, 6) and its image P′(5, 6) are marked; the mirror line is not drawn. Coordinate grid, all four quadrants, each square one unit, origin in the middle. Point P(-3, 6) and its image P′(5, 6) are marked; the mirror line is not drawn. −10 −8 −6 −4 −2 2 4 6 8 10 −10 −9 −8 −7 −6 −5 −4 −3 −2 −1 1 2 3 4 5 6 7 8 9 10 P P' A flip sends Tala's leaf marker from P(-7, 1) to P′(-1, 1). The mirror line is vertical (x = k). What is k?
Coordinate grid, all four quadrants, each square one unit, origin in the middle. Point P(-7, 1) and its image P′(-1, 1) are marked; the mirror line is not drawn. Coordinate grid, all four quadrants, each square one unit, origin in the middle. Point P(-7, 1) and its image P′(-1, 1) are marked; the mirror line is not drawn. −10 −8 −6 −4 −2 2 4 6 8 10 −10 −9 −8 −7 −6 −5 −4 −3 −2 −1 1 2 3 4 5 6 7 8 9 10 P P' A flip sends Zee's paper marker from P(6, -2) to P′(6, 8). The mirror line is horizontal (y = k). What is k?
Coordinate grid, all four quadrants, each square one unit, origin in the middle. Point P(6, -2) and its image P′(6, 8) are marked; the mirror line is not drawn. Coordinate grid, all four quadrants, each square one unit, origin in the middle. Point P(6, -2) and its image P′(6, 8) are marked; the mirror line is not drawn. −10 −8 −6 −4 −2 2 4 6 8 10 −10 −9 −8 −7 −6 −5 −4 −3 −2 −1 1 2 3 4 5 6 7 8 9 10 P P' Ari's rocket marker P(-2, 6) is flipped across the line x = 3 to P′. How many units long is segment PP′?
Coordinate grid, all four quadrants, each square one unit, origin in the middle. Point P(-2, 6) is marked and the mirror line x = 3 is drawn dashed; the image is not drawn. Coordinate grid, all four quadrants, each square one unit, origin in the middle. Point P(-2, 6) is marked and the mirror line x = 3 is drawn dashed; the image is not drawn. −10 −8 −6 −4 −2 2 4 6 8 10 −10 −9 −8 −7 −6 −5 −4 −3 −2 −1 1 2 3 4 5 6 7 8 9 10 x = 3 P Bo's robot marker P(7, -3) is flipped across the line y = 2 to P′. How many units long is segment PP′?
Coordinate grid, all four quadrants, each square one unit, origin in the middle. Point P(7, -3) is marked and the mirror line y = 2 is drawn dashed; the image is not drawn. Coordinate grid, all four quadrants, each square one unit, origin in the middle. Point P(7, -3) is marked and the mirror line y = 2 is drawn dashed; the image is not drawn. −10 −8 −6 −4 −2 2 4 6 8 10 −10 −9 −8 −7 −6 −5 −4 −3 −2 −1 1 2 3 4 5 6 7 8 9 10 y = 2 P Esme's shell marker P(-5, 1) is flipped across the line x = -1 to P′. How many units long is segment PP′?
Coordinate grid, all four quadrants, each square one unit, origin in the middle. Point P(-5, 1) is marked and the mirror line x = -1 is drawn dashed; the image is not drawn. Coordinate grid, all four quadrants, each square one unit, origin in the middle. Point P(-5, 1) is marked and the mirror line x = -1 is drawn dashed; the image is not drawn. −10 −8 −6 −4 −2 2 4 6 8 10 −10 −9 −8 −7 −6 −5 −4 −3 −2 −1 1 2 3 4 5 6 7 8 9 10 x = -1 P Jun's bus marker P(3, 6) is flipped across the line y = -2 to P′. How many units long is segment PP′?
Coordinate grid, all four quadrants, each square one unit, origin in the middle. Point P(3, 6) is marked and the mirror line y = -2 is drawn dashed; the image is not drawn. Coordinate grid, all four quadrants, each square one unit, origin in the middle. Point P(3, 6) is marked and the mirror line y = -2 is drawn dashed; the image is not drawn. −10 −8 −6 −4 −2 2 4 6 8 10 −10 −9 −8 −7 −6 −5 −4 −3 −2 −1 1 2 3 4 5 6 7 8 9 10 y = -2 P