Find the coordinates of A' and D if ABCDE∼A′B′C′D′E′, the center of dilation is F (-6,1), and the scale factor is 3. .
A (2,2), B (-2,2), C (-3,4), E (2,5), B' (6,4), C' (3,10), D' (9,19), and E' (18,13).
i really need help on this, thank you
the dilated points will be 3 times the distance from F as the original points
... the direction is along the line from F to the point being dilated
A' is 3 times farther from F than A , along the FA line
D is 1/3 the distance from F to D' , along the FD' line
F to A is ... 8 in x and 1 in y ... so F to A' is 3*8 in x and 3*1 in y
... A is [(24 - 6),(3 + 1)]
use the same technique for D
To find the coordinates of A' and D, we need to use the center of dilation (F) and the scale factor of 3.
Let's start with A.
To find A', we need to take the coordinates of A and apply the scale factor and translation.
Step 1: Scale A by a factor of 3.
The x-coordinate of A' will be (2 * 3) = 6.
The y-coordinate of A' will be (2 * 3) = 6.
Step 2: Translate A' by the vector from F to the origin.
The x-coordinate of F is -6, so we add -6 to the x-coordinate of A' to get -6 + 6 = 0.
The y-coordinate of F is 1, so we add 1 to the y-coordinate of A' to get 1 + 6 = 7.
Therefore, the coordinates of A' are (0, 7).
Now let's move on to D.
To find D', we'll follow the same steps as above.
Step 1: Scale D by a factor of 3.
The x-coordinate of D' will be (-3 * 3) = -9.
The y-coordinate of D' will be (4 * 3) = 12.
Step 2: Translate D' by the vector from F to the origin.
The x-coordinate of F is -6, so we add -6 to the x-coordinate of D' to get -9 - 6 = -15.
The y-coordinate of F is 1, so we add 1 to the y-coordinate of D' to get 12 + 1 = 13.
Therefore, the coordinates of D' are (-15, 13).
So, the coordinates of A' are (0,7) and the coordinates of D' are (-15,13).