Find the dilation of 0.5 with center (0,0) for the following points if A ( − 7 , 0 ) B (6,-6)
To find the dilation of a point, we can use the formula (x', y') = (kx, ky) where (x', y') is the dilated point, (x, y) is the original point, and k is the scale factor.
For point A (-7, 0), the dilated point can be found using the formula:
(x', y') = (0.5*(-7), 0.5*0) = (-3.5, 0)
For point B (6, -6), the dilated point can be found using the formula:
(x', y') = (0.5*6, 0.5*(-6)) = (3, -3)
Therefore, the dilated points are A' (-3.5, 0) and B' (3, -3).
Find the dilation of 2 with center (0,0) for the following points if A ( − 7 , -1 ) B (2,-7)
To find the dilation of a point, we can use the formula (x', y') = (kx, ky) where (x', y') is the dilated point, (x, y) is the original point, and k is the scale factor.
For point A (-7, -1), the dilated point can be found using the formula:
(x', y') = (2*(-7), 2*(-1)) = (-14, -2)
For point B (2, -7), the dilated point can be found using the formula:
(x', y') = (2*2, 2*(-7)) = (4, -14)
Therefore, the dilated points are A' (-14, -2) and B' (4, -14).
What is point A (6, 7) after a translation of 2 units left and 5 units down followed by a 180° clockwise rotation around the origin.
To perform a translation, we subtract the specified units from the x- and y-coordinates of the point.
After translating 2 units left and 5 units down, point A (6, 7) becomes:
A' (6 - 2, 7 - 5) = A' (4, 2)
To perform a 180° clockwise rotation around the origin, we take the negative of the x- and y-coordinates of the translated point.
After the rotation, point A' (4, 2) becomes:
A'' (-(4), -(2)) = A'' (-4, -2)
Therefore, point A (6, 7) after the translation and rotation is A'' (-4, -2).
What is point A (-7, -9) after a translation of 5 units left and 3 units up followed by a reflection over the x-axis
To perform a translation, we subtract the specified units from the x- and y-coordinates of the point.
After translating 5 units to the left and 3 units up, point A (-7, -9) becomes:
A' (-7 - 5, -9 + 3) = A' (-12, -6)
To perform a reflection over the x-axis, we change the sign of the y-coordinate.
After the reflection, point A' (-12, -6) becomes:
A'' (-12, -(-6)) = A'' (-12, 6)
Therefore, point A (-7, -9) after the translation and reflection is A'' (-12, 6).