Question

find the coordinates of the figure after
reflecting in the x-axis.
e(-1,0), f(-2,8), g(-7,6), h(-8,1)
e’: f’: g’: h’:

find the coordinates of the figure after
reflecting in the y-axis.
w(5,-1), x(4,-5), y(4,-4)
w’: x’: y’:

find the coordinates of the figure after
reflecting in the x-axis.
a(0,8), b(8,6), c(6,1), d(1,0)
a’: b’: c’: d’:

find the coordinates of the figure after
reflecting in the y-axis.
j(-1,-5), k(-5,-4), l(-4,-1)
w’: x’: y’:

find the coordinates of the figure after
reflecting in the x-axis.
a(-8,0), b(-1,8), c(-2,6), d(-7,1)
a’: b’: c’: d’:

find the coordinates of the figure after
reflecting in the y-axis.
j(5, -1), k(4, -5), l(4, -4)
w’: x’: y’:

Explanation:

First Reflection (x - axis) for E, F, G, H

Step1: Recall reflection over x - axis rule

The rule for reflecting a point \((x,y)\) over the \(x\) - axis is \((x,y)\to(x, -y)\).

Step2: Apply rule to E(-1,0)

For point \(E(-1,0)\), using the rule \((x,y)\to(x, -y)\), we substitute \(x=-1\) and \(y = 0\). So \(E'=(-1,-0)=(-1,0)\).

Step3: Apply rule to F(-2,8)

For point \(F(-2,8)\), substitute \(x = - 2\) and \(y=8\) into the rule. We get \(F'=(-2,-8)\).

Step4: Apply rule to G(-7,6)

For point \(G(-7,6)\), substitute \(x=-7\) and \(y = 6\) into the rule. We get \(G'=(-7,-6)\).

Step5: Apply rule to H(-8,1)

For point \(H(-8,1)\), substitute \(x=-8\) and \(y = 1\) into the rule. We get \(H'=(-8,-1)\).

First Reflection (y - axis) for W, X, Y

Step1: Recall reflection over y - axis rule

The rule for reflecting a point \((x,y)\) over the \(y\) - axis is \((x,y)\to(-x,y)\).

Step2: Apply rule to W(5,-1)

For point \(W(5,-1)\), substitute \(x = 5\) and \(y=-1\) into the rule. We get \(W'=(-5,-1)\).

Step3: Apply rule to X(4,-5)

For point \(X(4,-5)\), substitute \(x = 4\) and \(y=-5\) into the rule. We get \(X'=(-4,-5)\).

Step4: Apply rule to Y(4,-4)

For point \(Y(4,-4)\), substitute \(x = 4\) and \(y=-4\) into the rule. We get \(Y'=(-4,-4)\).

Second Reflection (x - axis) for A, B, C, D

Step1: Recall reflection over x - axis rule

The rule for reflecting a point \((x,y)\) over the \(x\) - axis is \((x,y)\to(x, -y)\).

Step2: Apply rule to A(0,8)

For point \(A(0,8)\), substitute \(x = 0\) and \(y = 8\) into the rule. We get \(A'=(0,-8)\).

Step3: Apply rule to B(8,6)

For point \(B(8,6)\), substitute \(x = 8\) and \(y = 6\) into the rule. We get \(B'=(8,-6)\).

Step4: Apply rule to C(6,1)

For point \(C(6,1)\), substitute \(x = 6\) and \(y = 1\) into the rule. We get \(C'=(6,-1)\).

Step5: Apply rule to D(1,0)

For point \(D(1,0)\), substitute \(x = 1\) and \(y = 0\) into the rule. We get \(D'=(1,0)\).

Second Reflection (y - axis) for J, K, L

Answer:

E'(-1, 0), F'(-2, -8), G'(-7, -6), H'(-8, -1)