To find the value of k, we need to determine the translation in the y-direction, or the change in the y-coordinate of the point.
From (-4, 1) to (4, 2), the y-coordinate increased by 1. Therefore, the value of k is 1.
Thus, the value of k is 1.
a point is translated on the coordinate plane from (-4,1) to (4,2). journey writes the function g(y) =y+k to describe the translations. what is the value of k?
11 answers
Triangle PQR is reflected over a vertical line of reflection to create triangle P'Q'R' . What are the coordinates of point R' ?
If triangle PQR is reflected over a vertical line of reflection, it means that the x-coordinate of each point is negated.
Let's say the coordinates of point R are (x, y). After the reflection over the vertical line, the x-coordinate gets negated, so the x-coordinate of R' will be -x. The y-coordinate remains the same.
Therefore, the coordinates of point R' will be (-x, y).
Let's say the coordinates of point R are (x, y). After the reflection over the vertical line, the x-coordinate gets negated, so the x-coordinate of R' will be -x. The y-coordinate remains the same.
Therefore, the coordinates of point R' will be (-x, y).
Triangle PQR is reflected over a vertical line of reflection to create triangle P'Q'R' . What are the coordinates of point R' ?
(-3,1)
(-2,7)
(1,-3)
(11,1)
(-3,1)
(-2,7)
(1,-3)
(11,1)
If triangle PQR is reflected over a vertical line of reflection, the x-coordinate of each point will be negated.
If the coordinates of point R are (x, y), the coordinates of point R' will be (-x, y).
Among the given options, neither (-3, 1), (-2, 7), nor (11, 1) have negated x-coordinates. The only option with a negated x-coordinate is (1, -3).
Therefore, the coordinates of point R' are (1, -3).
If the coordinates of point R are (x, y), the coordinates of point R' will be (-x, y).
Among the given options, neither (-3, 1), (-2, 7), nor (11, 1) have negated x-coordinates. The only option with a negated x-coordinate is (1, -3).
Therefore, the coordinates of point R' are (1, -3).
For triangle FUN, x= -1. what are the coordinates for F' after a reflection?
F'(5.-5)
F'(3,5)
F'(-1,4)
F'(-5,-5)
F'(5.-5)
F'(3,5)
F'(-1,4)
F'(-5,-5)
Since triangle FUN is reflected over the line x = -1, it means that all the x-coordinates of the points will be the negation of their original values.
Among the given options, F'(-1, 4) has the negated x-coordinate. Therefore, the coordinates for F' after the reflection are (-1, 4).
Among the given options, F'(-1, 4) has the negated x-coordinate. Therefore, the coordinates for F' after the reflection are (-1, 4).
The coordinate point Q(0,10) is reflected over the y-axis. identify the x- and y-coordinates of its image, Q'
When a point is reflected over the y-axis, its x-coordinate is negated while the y-coordinate remains the same.
The original coordinates of point Q are (0, 10). After reflecting over the y-axis, the x-coordinate will be negated, resulting in (-0, 10). However, we typically do not include the negative sign in front of zero, so the x-coordinate of the image, Q', is simply 0.
Therefore, the x-coordinate of point Q' is 0, while the y-coordinate remains 10.
Hence, the coordinates of point Q' are (0, 10).
The original coordinates of point Q are (0, 10). After reflecting over the y-axis, the x-coordinate will be negated, resulting in (-0, 10). However, we typically do not include the negative sign in front of zero, so the x-coordinate of the image, Q', is simply 0.
Therefore, the x-coordinate of point Q' is 0, while the y-coordinate remains 10.
Hence, the coordinates of point Q' are (0, 10).
a double reflection of a preimage across perpendicular lines produce the same result as a
single rotation of the preimage by 180 degrees about the point of intersection of the perpendicular lines.
In other words, if a preimage is reflected across one line and then reflected across another line perpendicular to the first, the resulting image will be the same as if the preimage was rotated by 180 degrees about the point of intersection of the two lines.
This is because reflecting a shape across a line is equivalent to rotating it by 180 degrees about a point on the line. When the shape is reflected across another line perpendicular to the first, it essentially rotates the shape by another 180 degrees, bringing it back to its original orientation.
So, a double reflection across perpendicular lines is equivalent to a single rotation of 180 degrees about their point of intersection.
In other words, if a preimage is reflected across one line and then reflected across another line perpendicular to the first, the resulting image will be the same as if the preimage was rotated by 180 degrees about the point of intersection of the two lines.
This is because reflecting a shape across a line is equivalent to rotating it by 180 degrees about a point on the line. When the shape is reflected across another line perpendicular to the first, it essentially rotates the shape by another 180 degrees, bringing it back to its original orientation.
So, a double reflection across perpendicular lines is equivalent to a single rotation of 180 degrees about their point of intersection.