graph the triangle abc after a 90 degree clockwise rotation around the center at origin

Question

A = (4, -3)
B = (4, 0)
C = (8, 0)

A' = (_, _)
B' = (_, _)
C' = (_, _)

Answer 1

To rotate a point (x, y) 90 degrees clockwise around the origin, the new coordinates are (-y, x).

So for each point:
A' = (-(-3), 4) = (3, 4)
B' = (0, 4)
C' = (0, 8)

Therefore, the triangle after a 90 degree clockwise rotation around the center at the origin would be:
A' = (3, 4)
B' = (0, 4)
C' = (0, 8)

Here is the graph of the original triangle ABC and the rotated triangle A'B'C':

graph LR
A(4,-3) --> B(4,0)
A(4,-3) --> C(8,0)
B(4,0) --> C(8,0)
A(4,-3) --> D(3,4)
B(4,0) --> E(0,4)
C(8,0) --> F(8,0)
D(3,4) --> E(0,4)
E(0,4) --> F(8,0)
F(8,0) --> D(3,4)

Answer 2

if AB = 18 inches then find the distance of A'B' after a reflection over the x-axis and a rotation of 226 degrees clockwise

A'B' = ___ inches

Answer 3

To find the distance of the new segment A'B' after a reflection over the x-axis and a rotation of 226 degrees clockwise, we first reflect the point A'B' over the x-axis. Since the x-axis is the line y = 0, the reflection of A'(3, 4) over the x-axis gives A''(3, -4).

Next, we rotate A''(3, -4) 226 degrees clockwise around the origin. To rotate a point (x, y) 226 degrees clockwise around the origin, the new coordinates are:

x' = x * cos(226°) + y * sin(226°)
y' = -x * sin(226°) + y * cos(226°)

Plugging in the values:
x' = 3 * cos(226°) + (-4) * sin(226°)
y' = -3 * sin(226°) + (-4) * cos(226°)

Calculating these values, we get:
x' ≈ -2.63
y' ≈ -1.91

Therefore, the coordinates of A' after the reflection over the x-axis and rotation of 226 degrees clockwise are A'(-2.63, -1.91).

Now, to find the distance of A'B', we can use the distance formula:

A'B' = √[(-2.63 - 3)^2 + (-1.91 - 4)^2]
A'B' = √[(-5.63)^2 + (-5.91)^2]
A'B' = √[31.61 + 35.08]
A'B' ≈ √66.69
A'B' ≈ 8.17 inches

Therefore, the distance of A'B' after a reflection over the x-axis and a rotation of 226 degrees clockwise is approximately 8.17 inches.

Answer 4

1.
What are the coordinate points for A' if A(4, 11) after being translated right 3 and up 6.
A' = ___

2.
What is point A (7, 7) after a translation of 3 units left and 5 units down followed by a 180 degree clockwise rotation around the origin.
(_, _)

3.
find the dilation of 4 with center (0, 0) for the following points if A (1, -1) B (-2, 6)
A' (_, _)
B' (_, _)

4.
what are the coordinate points of A' (6, 5) if A undergoes a rotation of:
90 degrees clockwise ____
180 degrees clockwise ____
270 degrees clockwise ____

5.
the diameter of a circle was 3 cm and the diameter of the final circle was 24 cm. what is the scale factor?
____

Answer 5

1. To find the coordinate points for A' if A(4, 11) is translated right 3 units and up 6 units:
A'(7, 17)

2. To find the point A(7, 7) after a translation of 3 units left and 5 units down followed by a 180-degree clockwise rotation around the origin:
Translate left 3 units and down 5 units: A'(4, 2)
Rotate 180 degrees around the origin: A'(-4, -2)

3. To find the dilation of 4 with center (0, 0) for the points A(1, -1) and B(-2, 6):
A'(4, -4)
B'(-8, 24)

4. To find the coordinate points of A' (6, 5) if A undergoes a rotation:
90 degrees clockwise: A'(-5, 6)
180 degrees clockwise: A'(-6, -5)
270 degrees clockwise: A'(5, -6)

5. To find the scale factor between a circle with a diameter of 3 cm and the final circle with a diameter of 24 cm:
Initial diameter = 3 cm
Final diameter = 24 cm
Scale factor = Final diameter / Initial diameter = 24 / 3 = 8

Therefore, the scale factor between the two circles is 8.

Answer 6

Find
�
′
A
′
and
�
′
B
′
if
�

(
6
,

−
2
)
A (6, −2) and
�

(
3
,

−
7
)
B (3, −7) is reflected over the x-axis.

Answer 7

When points are reflected over the x-axis, their y-coordinates change sign while their x-coordinates remain the same.

Given points:
A(6, -2)
B(3, -7)

After reflection over the x-axis:
A'(6, 2)
B'(3, 7)

Therefore, the coordinates for A' and B' after reflection over the x-axis are A'(6, 2) and B'(3, 7).