If point P (2,-8) is reflected across the line y = -2, what are the coordinates of its reflection image? Write your answer as a coordinate point. (2 points)

Answer 1

The line of reflection is y = -2.

To find the reflected point, we need to find the distance between point P and the line y = -2. This distance will be the same for both the original point and its reflection.

The distance between point P (2, -8) and the line y = -2 is 6 units (from -8 to -2).

Since the reflection will be the same distance from the line but on the opposite side, the reflected point will be 6 units above the line y = -2.

Therefore, the coordinates of the reflected point will be (2, 2).

Therefore, the coordinates of the reflection image are (-2, 2).

Answer 2

The vertices of a triangle are P(–7, –4), Q(–7, –8), and R(3, –3). Name the vertices of the image reflected across the line x axis.(3 points)

Answer 3

To reflect a point across the x-axis, we change the sign of the y-coordinate while keeping the x-coordinate the same.

For point P(–7, –4), the image point P' after reflecting across the x-axis will have the coordinates (–7, 4).

For point Q(–7, –8), the image point Q' after reflecting across the x-axis will have the coordinates (–7, 8).

For point R(3, –3), the image point R' after reflecting across the x-axis will have the coordinates (3, 3).

Therefore, the vertices of the new triangle after reflecting across the x-axis are P'(–7, 4), Q'(–7, 8), and R'(3, 3).

Answer 4

How many lines of symmetry are found in a regular polygon with 70 sides?(1 point)

Answer 5

A regular polygon with n sides has n lines of symmetry.

Therefore, a regular polygon with 70 sides will have 70 lines of symmetry.

Answer 6

A dilation has center (0, 0, 0). Find the image of the point (–2, –3, 0) for the scale factor of 3.

Answer 7

To find the image of the point (-2, -3, 0) after the dilation with center (0, 0, 0) and a scale factor of 3, we simply multiply the coordinates of the point by the scale factor.

Image of the point = (scale factor) * (original coordinates)

Image of the point = 3 * (-2, -3, 0)

Image of the point = (-6, -9, 0)

Therefore, the image of the point (-2, -3, 0) after dilation with a scale factor of 3 and center (0, 0, 0) is (-6, -9, 0).

Answer 8

The endpoints of AB¯¯¯¯¯¯¯¯ are A (8,4) and B(6,-2). The endpoints of its image after a dilation are A' (5,2.5) and B'(3.75,-1.25). Find the scale factor. Please enter your scale factor as a whole number or a fraction. No Decimals(3 points)

Answer 9

To find the scale factor of the dilation, we can compare the change in coordinates from the original to the image endpoints.

Let's first find the change in x and y coordinates for point A:
Change in x-coordinate for A: 5 - 8 = -3
Change in y-coordinate for A: 2.5 - 4 = -1.5

Let's now find the change in x and y coordinates for point B:
Change in x-coordinate for B: 3.75 - 6 = -2.25
Change in y-coordinate for B: -1.25 - (-2) = 0.75

Now, we can calculate the dilation scale factor:
Scale factor = Change in x-coordinate (A) / Change in x-coordinate (B)
Scale factor = -3 / -2.25
Scale factor = 4/3

Therefore, the scale factor for the dilation is 4/3.