Triangle DEF is dilated with respect to the origin by a scale factor of
to produce ΔD'E'F'. What is the length of side D'E'?
A Linear-quadratic of Triangle shape graph DEF with D as the Origin Scale of Factor 1 by 3. The D intersects at X equals 0 and Y equals 9, E interests at X equals 3 and Y equals 3 and F intersecting at X equals 9 and Y equals 3.
Based on the given information, we can find the coordinates of D', E', and F', which are the corresponding points after the dilation.
Since the scale factor is 3, we can multiply the x-coordinate and y-coordinate of each point by 3 to find the corresponding point.
Coordinates of D' = (3*0, 3*9) = (0, 27)
Coordinates of E' = (3*3, 3*3) = (9, 9)
Coordinates of F' = (3*9, 3*3) = (27, 9)
Now, we can calculate the length of side D'E' using the distance formula.
Length of D'E' = √[(x2 - x1)^2 + (y2 - y1)^2]
= √[(9 - 0)^2 + (9 - 27)^2]
= √[81 + 324]
= √405
= 3√45
Therefore, the length of side D'E' is 3√45.