When a point is reflected over the x-axis, the x-coordinate remains the same, but the y-coordinate is flipped in sign.
For point A (0, -1), the x-coordinate remains 0, but the y-coordinate changes to 1. Therefore, A' is (0, 1).
For point B (-1, 1), the x-coordinate remains -1, but the y-coordinate changes to -1. Therefore, B' is (-1, -1).
Find A' and B' if A (0,-1) and B (-1,1) is reflected over the x-axis.
A'=
B'=
11 answers
Find A' and B' if A (1,-10) and B (4,-10) is reflected over the y-axis.
A'=
B'=
A'=
B'=
When a point is reflected over the y-axis, the y-coordinate remains the same, but the x-coordinate is flipped in sign.
For point A (1, -10), the y-coordinate remains -10, but the x-coordinate changes to -1. Therefore, A' is (-1, -10).
For point B (4, -10), the y-coordinate remains -10, but the x-coordinate changes to -4. Therefore, B' is (-4, -10).
For point A (1, -10), the y-coordinate remains -10, but the x-coordinate changes to -1. Therefore, A' is (-1, -10).
For point B (4, -10), the y-coordinate remains -10, but the x-coordinate changes to -4. Therefore, B' is (-4, -10).
what are the coordinate points of A' (3,3) if A undergoes a rotation of:
90° counterclockwise =
207° counterclockwise =
90° counterclockwise =
207° counterclockwise =
To rotate a point counterclockwise by 90 degrees, we swap the x and y coordinates and negate the new x coordinate.
For point A (3, 3), applying a 90° counterclockwise rotation:
A' = (-3, 3)
For a rotation of 207° counterclockwise, we can calculate this by breaking it down as follows: 207° = 180° + 27°.
A 180° rotation is equivalent to reflecting the point through the origin, so the x and y coordinates will just have their signs reversed:
A' = (-3, -3)
Now, to rotate the point A' (-3, -3) by an additional 27° counterclockwise, we'll have to use trigonometry. But before we do that, let's draw the xy coordinate axes and locate point A' (-3, -3).
Now, starting from point A' (-3, -3), measure an angle of 27° counterclockwise. Then drop a vertical line from A' (-3, -3) to the x-axis, and the intersection point will be the new rotated point.
Unfortunately, I'm unable to draw diagrams here, but trust that by approximating the location of point A' (-3, -3) in your own diagram, then measuring and rotating 27° counterclockwise, you can estimate the new coordinate point, which will be close to (2, -5).
For point A (3, 3), applying a 90° counterclockwise rotation:
A' = (-3, 3)
For a rotation of 207° counterclockwise, we can calculate this by breaking it down as follows: 207° = 180° + 27°.
A 180° rotation is equivalent to reflecting the point through the origin, so the x and y coordinates will just have their signs reversed:
A' = (-3, -3)
Now, to rotate the point A' (-3, -3) by an additional 27° counterclockwise, we'll have to use trigonometry. But before we do that, let's draw the xy coordinate axes and locate point A' (-3, -3).
Now, starting from point A' (-3, -3), measure an angle of 27° counterclockwise. Then drop a vertical line from A' (-3, -3) to the x-axis, and the intersection point will be the new rotated point.
Unfortunately, I'm unable to draw diagrams here, but trust that by approximating the location of point A' (-3, -3) in your own diagram, then measuring and rotating 27° counterclockwise, you can estimate the new coordinate point, which will be close to (2, -5).
what are the coordinate points of A' (1,9) if A undergoes a rotation of:
90° clockwise
90° clockwise
To rotate a point clockwise by 90 degrees, we swap the x and y coordinates and negate the new y coordinate.
For point A (1, 9), applying a 90° clockwise rotation:
A' = (9, -1)
For point A (1, 9), applying a 90° clockwise rotation:
A' = (9, -1)
What are the coordinate points of A' (5,6) if A undergoes a rotation of
180° clockwise
180° clockwise
To rotate a point clockwise by 180 degrees, we negate both the x and y coordinates.
For point A (5, 6), applying a 180° clockwise rotation:
A' = (-5, -6)
For point A (5, 6), applying a 180° clockwise rotation:
A' = (-5, -6)
if AB= 17 inches then find the distance of A′B′ after a reflection over the x-axis and a translation of (x+4, y−5).
A'B'=_____inches.
A'B'=_____inches.
When a point is reflected over the x-axis, the x-coordinate remains the same, but the y-coordinate is flipped in sign. So A' would have the same x-coordinate as A, but the y-coordinate would be -1 * y-coordinate of A.
After the reflection over the x-axis, A' would have coordinates (5, -6).
Now, we perform a translation of (x+4, y-5). This means we add 4 to the x-coordinate and subtract 5 from the y-coordinate.
The new coordinates of A' after the translation would be:
x-coordinate: 5 + 4 = 9
y-coordinate: -6 - 5 = -11
So, A' after the reflection over the x-axis and the translation of (x+4, y-5) would have coordinates (9, -11).
To find the distance A'B', we use the distance formula:
Distance = sqrt((x2 - x1)^2 + (y2 - y1)^2)
Using the coordinates of A' (9, -11) and B' (x+4, y-5), the distance of A'B' is:
Distance = sqrt((x+4 - 9)^2 + (y-5 - (-11))^2)
Since we do not have the specific values of x and y, we cannot determine the exact distance of A'B'.
After the reflection over the x-axis, A' would have coordinates (5, -6).
Now, we perform a translation of (x+4, y-5). This means we add 4 to the x-coordinate and subtract 5 from the y-coordinate.
The new coordinates of A' after the translation would be:
x-coordinate: 5 + 4 = 9
y-coordinate: -6 - 5 = -11
So, A' after the reflection over the x-axis and the translation of (x+4, y-5) would have coordinates (9, -11).
To find the distance A'B', we use the distance formula:
Distance = sqrt((x2 - x1)^2 + (y2 - y1)^2)
Using the coordinates of A' (9, -11) and B' (x+4, y-5), the distance of A'B' is:
Distance = sqrt((x+4 - 9)^2 + (y-5 - (-11))^2)
Since we do not have the specific values of x and y, we cannot determine the exact distance of A'B'.