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.
A.
B.
C.
D.
In this problem, the scale factor is not given, so it is not possible to determine the length of side D'E' without additional information.
To find the length of side D'E', we need to determine the coordinates of points D' and E' after the dilation.
Given the scale factor of , we can multiply the coordinates of D (0, 9) and E (3, 3) by the scale factor to find D' and E'.
D' = (0 * , 9 *) = (0, )
E' = (3 * , 3 *) = (3, )
Now, we can use the coordinates of D' and E' to calculate the length of side D'E':
Length of D'E' = √[(x₂ - x₁)² + (y₂ - y₁)²]
Where (x₁, y₁) = D' and (x₂, y₂) = E'.
Length of D'E' = √[(3 - 0)² + (- - )²]
However, there seems to be a missing value for the scale factor. Please provide the missing value so that I can help you complete the calculation.
To find the length of side D'E', we need to determine the coordinates of point D' and E' after the dilation.
Given that the triangle DEF is dilated with respect to the origin by a scale factor of , we can find the coordinates of D' and E' using the formula:
D' = (x * , y *)
E' = (x * , y *)
Let's substitute the coordinates of D and E into the formula:
D' = (0 * , 9 *)
E' = (3 * , 3 *)
Simplifying, we get:
D' = (0, 9)
E' = (3, 3)
Now that we have the coordinates of D' and E', we can use the distance formula to find the length of side D'E'. The distance formula is given by:
Distance = √((x₂ - x₁)² + (y₂ - y₁)²)
Substituting the coordinates of D' and E' into the formula:
Distance = √((3 - 0)² + (3 - 9)²)
= √(3² + (-6)²)
= √(9 + 36)
= √45
Therefore, the length of side D'E' is √45.
Looking at the answer choices, it seems that they are missing. Please provide the answer choices so that we can determine the correct option.