Question

Graph the triangle ABC after a 90-clockwise rotation around the center at the origin.

Answer 1

if ′A′B′ 30 inches then find the distance of ′A′B′ after a reflection over the x-axis and a rotation of 341° clockwise.

Answer 2

To graph the triangle ABC after a 90-clockwise rotation around the origin, we need to rotate each of its three vertices 90 degrees clockwise around the origin.

Let's say the coordinates of point A are (x1, y1), the coordinates of point B are (x2, y2), and the coordinates of point C are (x3, y3).

To rotate a point (x, y) 90 degrees clockwise around the origin, we can use the following formulas:

x' = y
y' = -x

Applying these formulas to each vertex of the triangle, we get:

A' = (y1, -x1)
B' = (y2, -x2)
C' = (y3, -x3)

Thus, the coordinates of the rotated triangle ABC are:

A' = (y1, -x1)
B' = (y2, -x2)
C' = (y3, -x3)

To visualize the rotation, you can plot the original triangle ABC and then plot the rotated triangle ABC' on the same coordinate plane.

Answer 3

To find the distance of A'B' after a reflection over the x-axis and a rotation of 341° clockwise, we need to perform the two transformations on the segment AB and then measure the length of the resulting segment.

1. Reflection over the x-axis:
A' = (x1, -y1)
B' = (x2, -y2)

2. Rotation of 341° clockwise:
To rotate a point (x, y) 341° clockwise around the origin, we can use the following formulas:

x' = x * cos(theta) + y * sin(theta)
y' = -x * sin(theta) + y * cos(theta)

Here, theta = 341° or 341 * ( π/180 ) radians.

Applying these formulas to each endpoint of the segment A'B', we get:

A'' = (A'x * cos(theta) + A'y * sin(theta), -A'x * sin(theta) + A'y * cos(theta))
B'' = (B'x * cos(theta) + B'y * sin(theta), -B'x * sin(theta) + B'y * cos(theta))

Finally, we can calculate the distance between A'' and B'' to find the length of A'B''.

A'B'' = sqrt((A''x - B''x)^2 + (A''y - B''y)^2)

Make sure to substitute the appropriate coordinates into the formulas to find the final distance.