Question

lesson 2 | session 5
2 point d is shown in the coordinate plane. plot the image point for each single transformation of point d. then write the coordinates.
a. image a: reflection across the x - axis
b. image b: translation 7 units to the right
c. image c: rotation 90° counterclockwise around the origin

Explanation:

1. First, assume the coordinates of point \(D\) are \((x,y)\).

• a. Reflection across the \(x -\)axis:
• # Explanation:

Step1: Recall reflection rule

The rule for reflecting a point \((x,y)\) across the \(x -\)axis is \((x,-y)\).
Let the coordinates of point \(D\) be \((x_D,y_D)\). The coordinates of image \(A\) will be \((x_D, - y_D)\).

• # Answer:

If \(D=(x_D,y_D)\), then \(A=(x_D, - y_D)\)

• b. Translation 7 units to the right:
• # Explanation:

Step1: Recall translation rule

The rule for translating a point \((x,y)\) \(h\) units to the right is \((x + h,y)\). Here \(h = 7\).
Let the coordinates of point \(D\) be \((x_D,y_D)\). The coordinates of image \(B\) will be \((x_D+7,y_D)\).

• # Answer:

If \(D=(x_D,y_D)\), then \(B=(x_D + 7,y_D)\)

• c. Rotation \(90^{\circ}\) counter - clockwise around the origin:
• # Explanation:

Step1: Recall rotation rule

The rule for rotating a point \((x,y)\) \(90^{\circ}\) counter - clockwise around the origin is \((-y,x)\).
Let the coordinates of point \(D\) be \((x_D,y_D)\). The coordinates of image \(C\) will be \((-y_D,x_D)\).

• # Answer:

If \(D=(x_D,y_D)\), then \(C=(-y_D,x_D)\)

Answer:

1. First, assume the coordinates of point \(D\) are \((x,y)\).

• a. Reflection across the \(x -\)axis:
• # Explanation:

Step1: Recall reflection rule

The rule for reflecting a point \((x,y)\) across the \(x -\)axis is \((x,-y)\).
Let the coordinates of point \(D\) be \((x_D,y_D)\). The coordinates of image \(A\) will be \((x_D, - y_D)\).

• # Answer:

If \(D=(x_D,y_D)\), then \(A=(x_D, - y_D)\)

• b. Translation 7 units to the right:
• # Explanation:

Step1: Recall translation rule

The rule for translating a point \((x,y)\) \(h\) units to the right is \((x + h,y)\). Here \(h = 7\).
Let the coordinates of point \(D\) be \((x_D,y_D)\). The coordinates of image \(B\) will be \((x_D+7,y_D)\).

• # Answer:

If \(D=(x_D,y_D)\), then \(B=(x_D + 7,y_D)\)

• c. Rotation \(90^{\circ}\) counter - clockwise around the origin:
• # Explanation:

Step1: Recall rotation rule

The rule for rotating a point \((x,y)\) \(90^{\circ}\) counter - clockwise around the origin is \((-y,x)\).
Let the coordinates of point \(D\) be \((x_D,y_D)\). The coordinates of image \(C\) will be \((-y_D,x_D)\).

• # Answer:

If \(D=(x_D,y_D)\), then \(C=(-y_D,x_D)\)