Question

1. translate the parallelogram by the rule (x − 8, y − 4). then reflect over the x -axis. plot all points and connect the lines.

ordered pairs: a = ____ b = __ c = __ d = ____

ordered pairs: a = ____ b = __ c = __ d = ____

ordered pairs: a = ____ b = __ c = __ d = ____

Explanation:

Step1: Find original coordinates

From the graph, identify the coordinates of each vertex:

• A: (2, 3) (since it's 2 units right on x - axis, 3 units up on y - axis)
• B: (7, 3) (7 units right on x - axis, 3 units up on y - axis)
• C: (6, 1) (6 units right on x - axis, 1 unit up on y - axis)
• D: (1, 1) (1 unit right on x - axis, 1 unit up on y - axis)

Step2: Apply translation rule \((x - 8,y - 4)\)

For a point \((x,y)\), the translated point \((x',y')=(x - 8,y - 4)\)

• For A(2, 3): \(x'=2 - 8=-6\), \(y'=3 - 4=-1\), so A'=(-6, -1)
• For B(7, 3): \(x'=7 - 8=-1\), \(y'=3 - 4=-1\), so B'=(-1, -1)
• For C(6, 1): \(x'=6 - 8=-2\), \(y'=1 - 4=-3\), so C'=(-2, -3)
• For D(1, 1): \(x'=1 - 8=-7\), \(y'=1 - 4=-3\), so D'=(-7, -3)

Step3: Apply reflection over x - axis

The rule for reflection over x - axis is \((x,y)\to(x, -y)\)

• For A'(-6, -1): \(x=-6\), \(y=-(-1)=1\), so A''=(-6, 1)
• For B'(-1, -1): \(x=-1\), \(y=-(-1)=1\), so B''=(-1, 1)
• For C'(-2, -3): \(x=-2\), \(y=-(-3)=3\), so C''=(-2, 3)
• For D'(-7, -3): \(x=-7\), \(y=-(-3)=3\), so D''=(-7, 3)

Answer:

Original Ordered Pairs:
A = (2, 3)
B = (7, 3)
C = (6, 1)
D = (1, 1)

Translated Ordered Pairs:
A' = (-6, -1)
B' = (-1, -1)
C' = (-2, -3)
D' = (-7, -3)

Reflected Ordered Pairs:
A'' = (-6, 1)
B'' = (-1, 1)
C'' = (-2, 3)
D'' = (-7, 3)