Question

drag the tiles to the boxes to form correct pairs. quadrilateral abcd has vertices a(-3, 4), b(1, 3), c(3, 6), and d(1, 6). match each set of vertices of quadrilateral efgh with the transformation that shows it is congruent to abcd. e(-3, -4), f(1, -3), g(3, -6), and h(1, -6) a translation 7 units right e(-3, -1), f(1, -2), g(3, 1), and h(1, 1) a reflection across the y - axis e(3, 4), f(-1, 3), g(-3, 6), and h(-1, 6) a reflection across the x - axis e(4, 4), f(8, 3), g(10, 6), and h(8, 6) translation 5 units down

Explanation:

Step1: Recall transformation rules

• Reflection across x - axis: $(x,y)\to(x, - y)$
• Reflection across y - axis: $(x,y)\to(-x,y)$
• Translation right by $a$ units: $(x,y)\to(x + a,y)$
• Translation down by $b$ units: $(x,y)\to(x,y - b)$

Step2: Analyze first set of vertices

For $E(-3,-4),F(1,-3),G(3,-6),H(1,-6)$ compared to $A(-3,4),B(1,3),C(3,6),D(1,6)$, the x - coordinates remain the same and the y - coordinates are negated. So it is a reflection across the x - axis.

Step3: Analyze second set of vertices

For $E(-3,-1),F(1,-2),G(3,1),H(1,1)$, $y$ - coordinates of $A,B,C,D$ are decreased by 5 ($4-5=-1,3 - 5=-2,6-5 = 1$). So it is a translation 5 units down.

Step4: Analyze third set of vertices

For $E(3,4),F(-1,3),G(-3,6),H(-1,6)$, the x - coordinates of $A,B,C,D$ are negated. So it is a reflection across the y - axis.

Step5: Analyze fourth set of vertices

For $E(4,4),F(8,3),G(10,6),H(8,6)$, the x - coordinates of $A(-3,4),B(1,3),C(3,6),D(1,6)$ are increased by 7 ($-3 + 7=4,1+7 = 8,3+7=10,1 + 7=8$). So it is a translation 7 units right.

Answer:

$E(-3,-4),F(1,-3),G(3,-6),H(1,-6)$ $\longleftrightarrow$ a reflection across the x - axis
$E(-3,-1),F(1,-2),G(3,1),H(1,1)$ $\longleftrightarrow$ a translation 5 units down
$E(3,4),F(-1,3),G(-3,6),H(-1,6)$ $\longleftrightarrow$ a reflection across the y - axis
$E(4,4),F(8,3),G(10,6),H(8,6)$ $\longleftrightarrow$ a translation 7 units right