Answer:
The length of segment QM' = 6
Step-by-step explanation:
Given:
Q is the center of dilation
Pre-image (original image) = segment LM
New image = segment L'M'
The length of LQ = 4
The length of QM = 3
The length of LL' = 4
The original image was dilated with scale factor = 2
QM' = ?
To determine segment QM', first we would draw the diagram obtained from the given information.
Find attached the diagram
When a figure is dilated, we would have similar shape in thus cars similar triangles.
Segment L'M' = scale factor × length of LM
Let LM = x
L'M' = 2x
Using similar triangles theorem, ratio of their corresponding sides are equal.
QM/LM = QM'/L'M'
3/x = QM'/2x
6x = QM' × x
Q'M' = 6
The length of segment QM' = 6
Answer:
Shown Below
Step-by-step explanation:
Alright so first off we are going to use the little 67 on that corner. We know that it's a supplementary angle, and supplementary angles add up to 180.
180 - 67 = 113.
Inside angles of a triangle all add up to 180. Using that we can create the equation:
(x + 27) + x + 113 = 180
simplify.
2x + 140 = 180
subtract 140 on both sides.
2x = 40
divide both sides by 2
x = 20
substitute x into the asked equation.
(20 + 27) = 47
47 is your answer.