What is scale factor for the dilation of segment AB into segment CD?
Draw the dilation of segment AB with scale factor 2/3 and label it segment EF.
The figure is 2 || segments with point A(3, -3) with B(6,3). Other segment is C(4,-4) with D(8,4). Cant seem to get it figured out. Need help.
the length of AB is √45 = 3√5
the length of CD is √80 = 4√5
So, since dilations scale lengths linearly, CD/AB = 4/3
No idea what EF is supposed to be for...
To find the scale factor for the dilation of segment AB into segment CD, we can use the formula:
Scale factor = Length of image segment / Length of original segment
For segment AB, the coordinates are A(3, -3) and B(6, 3), so we can calculate its length using the distance formula:
Length of AB = sqrt((x2 - x1)^2 + (y2 - y1)^2)
= sqrt((6 - 3)^2 + (3 - (-3))^2)
= sqrt(3^2 + 6^2)
= sqrt(9 + 36)
= sqrt(45)
= 3√5
Now, let's calculate the length of segment CD. The coordinates for C and D are C(4, -4) and D(8, 4), respectively:
Length of CD = sqrt((x2 - x1)^2 + (y2 - y1)^2)
= sqrt((8 - 4)^2 + (4 - (-4))^2)
= sqrt(4^2 + 8^2)
= sqrt(16 + 64)
= sqrt(80)
= 4√5
Finally, we can determine the scale factor:
Scale factor = Length of CD / Length of AB
= (4√5) / (3√5)
= 4/3
Therefore, the scale factor for the dilation of segment AB into segment CD is 4/3.
To draw the dilation of segment AB with a scale factor of 2/3, we can start by plotting the values of segment AB. Then, we can multiply the coordinates of each point by the scale factor to get the coordinates of segment EF.
Let's calculate the coordinates of segment EF:
For point E:
xE = 3 * (2/3) = 2
yE = -3 * (2/3) = -2
For point F:
xF = 6 * (2/3) = 4
yF = 3 * (2/3) = 2
So, the coordinates of segment EF are E(2, -2) and F(4, 2).
Now, you can draw segment EF on your figure, labeled as segment EF.
To find the scale factor for the dilation of segment AB into segment CD, you can use the formula:
Scale factor = Length of the dilated segment / Length of the original segment
Let's calculate the lengths of segment AB and segment CD:
Length of segment AB = √((x₂ - x₁)² + (y₂ - y₁)²)
= √((6 - 3)² + (3 - (-3))²)
= √(3² + 6²)
= √(9 + 36)
= √45
= 3√5
Length of segment CD = √((x₂ - x₁)² + (y₂ - y₁)²)
= √((8 - 4)² + (4 - (-4))²)
= √(4² + 8²)
= √(16 + 64)
= √80
= 4√5
Now, substitute the lengths into the scale factor formula:
Scale factor = Length of segment CD / Length of segment AB
= (4√5) / (3√5)
= (4 / 3) * (√5 / √5)
= 4/3
Therefore, the scale factor for the dilation of segment AB into segment CD is 4/3.