Question

(x, y) \boldsymbol{\
ightarrow} (x-4, y+2)\
coordinate grid with triangle abc: a, b, c plotted on the grid

Explanation:

To solve the problem of finding the coordinates of the vertices after the transformation \((x, y) \to (x - 4, y + 2)\), we first need to determine the original coordinates of points \(A\), \(B\), and \(C\) from the graph.

Step 1: Identify Original Coordinates

• From the graph, we can see:
• Point \(A\) is at \((1, -1)\) (assuming the grid has integer coordinates, with the origin at the intersection of the axes).
• Point \(B\) is at \((3, 0)\).
• Point \(C\) is at \((4, -3)\).

Step 2: Apply the Transformation \((x, y) \to (x - 4, y + 2)\)

For each point, we substitute \(x\) and \(y\) into the transformation formula.

For Point \(A(1, -1)\):

• New \(x\)-coordinate: \(1 - 4 = -3\)
• New \(y\)-coordinate: \(-1 + 2 = 1\)
• So, the image of \(A\) is \((-3, 1)\).

For Point \(B(3, 0)\):

• New \(x\)-coordinate: \(3 - 4 = -1\)
• New \(y\)-coordinate: \(0 + 2 = 2\)
• So, the image of \(B\) is \((-1, 2)\).

For Point \(C(4, -3)\):

• New \(x\)-coordinate: \(4 - 4 = 0\)
• New \(y\)-coordinate: \(-3 + 2 = -1\)
• So, the image of \(C\) is \((0, -1)\).

If the question was to find the image of the points after the transformation, the answers are:

• Image of \(A\): \(\boldsymbol{(-3, 1)}\)
• Image of \(B\): \(\boldsymbol{(-1, 2)}\)
• Image of \(C\): \(\boldsymbol{(0, -1)}\)

Answer:

To solve the problem of finding the coordinates of the vertices after the transformation \((x, y) \to (x - 4, y + 2)\), we first need to determine the original coordinates of points \(A\), \(B\), and \(C\) from the graph.

Step 1: Identify Original Coordinates

• From the graph, we can see:
• Point \(A\) is at \((1, -1)\) (assuming the grid has integer coordinates, with the origin at the intersection of the axes).
• Point \(B\) is at \((3, 0)\).
• Point \(C\) is at \((4, -3)\).

Step 2: Apply the Transformation \((x, y) \to (x - 4, y + 2)\)

For each point, we substitute \(x\) and \(y\) into the transformation formula.

For Point \(A(1, -1)\):

• New \(x\)-coordinate: \(1 - 4 = -3\)
• New \(y\)-coordinate: \(-1 + 2 = 1\)
• So, the image of \(A\) is \((-3, 1)\).

For Point \(B(3, 0)\):

• New \(x\)-coordinate: \(3 - 4 = -1\)
• New \(y\)-coordinate: \(0 + 2 = 2\)
• So, the image of \(B\) is \((-1, 2)\).

For Point \(C(4, -3)\):

• New \(x\)-coordinate: \(4 - 4 = 0\)
• New \(y\)-coordinate: \(-3 + 2 = -1\)
• So, the image of \(C\) is \((0, -1)\).

If the question was to find the image of the points after the transformation, the answers are:

• Image of \(A\): \(\boldsymbol{(-3, 1)}\)
• Image of \(B\): \(\boldsymbol{(-1, 2)}\)
• Image of \(C\): \(\boldsymbol{(0, -1)}\)