Question

figure jklm is transformed using the rule ((x, y) \to (-x, y)).
image of a coordinate grid with figure jklm
which coordinate would be found on the transformed figure (jklm)?
(circ) ((1, -5))
(circ) ((4,1))
(circ) ((6,2))
(circ) ((-4, -1))

Explanation:

Step1: Identify original coordinates

First, find the coordinates of the original figure \(JKLM\) from the graph. Let's assume the coordinates (by looking at the grid):

• \(J\): Let's say \(J(-4, 1)\) (since it's at \(x = -4\), \(y = 1\))
• \(K\): Maybe \(K(-5, 4)\)
• \(L\): Maybe \(L(-2, 6)\)
• \(M\): Maybe \(M(-1, 4)\) (these are approximate from the grid, but we can use the transformation rule \((x, y) \to (-x, y)\))

Step2: Apply transformation rule

The transformation rule is \((x, y) \to (-x, y)\). So for each original point \((x, y)\), the transformed point is \((-x, y)\).

Let's check each option by reversing the transformation (since we need to see if a point \((a, b)\) on the transformed figure comes from an original point \((-a, b)\) on \(JKLM\)):

• For option \((1, -5)\): Reverse transformation would be \((-1, -5)\). But original figure has \(y\)-coordinates positive (from the graph), so unlikely.
• For option \((4, 1)\): Reverse transformation is \((-4, 1)\). Let's check if \((-4, 1)\) is on \(JKLM\). From the graph, \(J\) seems to be \((-4, 1)\), so applying the transformation \((-4, 1) \to (4, 1)\), which is this option.
• For option \((6, 2)\): Reverse transformation is \((-6, 2)\). Not on original figure.
• For option \((-4, -1)\): Reverse transformation is \((4, -1)\). Original figure has positive \(y\)-coordinates, so no.

Answer:

\( (4, 1) \)