Question

(a) the arrows below show that the coordinates on the left are mapped to the coordinat on the right. fill in the blanks to give the coordinates after the reflection. original coordinates → final coordinates ( d(-8,-4)
ightarrow d^{prime}(square, square) ) ( e(2,-3)
ightarrow e^{prime}(square, square) ) ( f(-5,-7)
ightarrow f^{prime}(square, square) ) (b) choose the general rule below that describes the reflection mapping ( \triangle d e f ) to ( \triangle d^{prime} e^{prime} f^{prime} )

Explanation:

Step1: Identify the reflection axis

From the graph, we can see that the reflection is about the \(x -\)axis. The rule for reflection about the \(x -\)axis is \((x,y)\to(x, - y)\).

Step2: Apply the reflection rule to each point

• For point \(D(-8,-4)\):

Using the rule \((x,y)\to(x, - y)\), when \(x=-8\) and \(y = - 4\), we get \(D'(-8,4)\).

• For point \(E(2,-3)\):

Using the rule \((x,y)\to(x, - y)\), when \(x = 2\) and \(y=-3\), we get \(E'(2,3)\).

• For point \(F(-5,-7)\):

Using the rule \((x,y)\to(x, - y)\), when \(x=-5\) and \(y = - 7\), we get \(F'(-5,7)\).

Answer:

\(D(-8,-4)\to D'(-8,4)\)
\(E(2,-3)\to E'(2,3)\)
\(F(-5,-7)\to F'(-5,7)\)