Question

a. write a rule for the congruence mapping that will move a figure 5 units to the right and 3 units up. b. write a rule for congruence mapping that reflects a figure across the y-axis.c. why are these mappings called congruence mappings?

Answer 1

Answer:
`\begin{gathered} a)\text{ }(x,\text{ y\rparen }\rightarrow\text{ \lparen x + 5, y + 3\rparen} \\ b)\text{ \lparen x, y\rparen }\rightarrow\text{ \lparen-x, y\rparen} \\ c)\text{ shape and size of the two figures are equal but different positions or orientation} \end{gathered}`

Step-by-step explanation:

Given:

Two different congruency mapping

To find:

a) a rule for the congruence mapping that will move a figure 5 units to the right and 3 units up

b) a rule for congruence mapping that reflects a figure across the y-axis

`\begin{gathered} a)\text{ Translation rule to the right:} \\ f(x\text{ -d\rparen: \lparen x, y\rparen }\rightarrow\text{ \lparen x+d, y\rparen} \\ Translation\text{ rule up:} \\ f(x)\text{ + b: \lparen x, y\rparen }\rightarrow\text{ \lparen x, y + b\rparen} \\ \\ 5\text{ units to the right and 3 units up:} \\ (x,\text{ y\rparen }\rightarrow\text{ \lparen x + 5, y + 3\rparen} \end{gathered}`
`\begin{gathered} b)\text{ reflection across the y-axis} \\ The\text{ x coordinate will be negated while the x coordinate will remain constant} \\ (x,\text{ y\rparen }\rightarrow\text{ \lparen-x, y\rparen} \end{gathered}`
`\begin{gathered} c)\text{ The mappings are called congruence mapping because the shapes and size remain the same } \\ \text{but the }position\text{ changes.} \\ As\text{ a result the corresponding angles and sides will be equal} \end{gathered}`