Given A(3, 2), B(-4, 1), and C(6, -5) translate the 4 unit to the left and 1 unit up followed by a dilation of 3. What are the new coordinates of B''?
Question
Given the points
- A(3, 2)
- B(-4, 1)
- C(6, -5)
Translate the points 4 units to the left and 1 unit up followed by a dilation of 3. What are the new coordinates of B''?
Solution
Step 1: Translation The first step is to translate the point B(-4, 1) 4 units to the left and 1 unit up.
To translate a point to the left, we subtract from the x-coordinate. To translate a point up, we add to the y-coordinate.
So, B' = B - 4 units left + 1 unit up = (-4-4, 1+1) = (-8, 2)
Step 2: Dilation The second step is to dilate the point B'(-8, 2) by a factor of 3.
To dilate a point, we multiply both the x-coordinate and the y-coordinate by the factor of dilation.
So, B'' = 3 * B' = 3 * (-8, 2) = (-24, 6)
Therefore, the new coordinates of B'' after the translation and dilation are (-24, 6).
Similar Questions
What is the image of the point A(3, -4) under the dilation by factor 2 with center of dilation at the origin followed by translation by the vector (-1, 1)
The point C(2,6) is translated 2 units right. What are the coordinates of the resulting point, C'?
The point T(4,–5) is translated 3 units up. What are the coordinates of the resulting point, T'?
The point D(6,3) is translated 4 units left and 9 units down. What are the coordinates of the resulting point, D'?
Given ABC at A (-3, 2), B (-1, 3), C (-4, 5), and if the is first reflected over the y-axis, and then over the x-axis, find the coordinate ofA''.
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.