The two triangles below are similar (but not drawn to scale). Find the value of x.x . Round answer to the nearest tenth.
36.9 inches,24.5 inches
11.7 inches ,x
To determine the value of x, we can set up a proportion using the corresponding sides of the two similar triangles:
36.9/24.5 = 11.7/x
Cross multiplying, we get:
36.9x = 24.5 * 11.7
Simplifying:
36.9x = 286.65
Dividing both sides by 36.9:
x = 286.65/36.9
x ≈ 7.8 inches
Therefore, the value of x is approximately 7.8 inches.
The hypotenuse of a triangle was 5 cm and the hypotenuse of the final triangle was 4.5 cm. What is the scale factor?
The scale factor can be determined by dividing the length of the final hypotenuse by the length of the original hypotenuse:
Scale factor = 4.5 cm/ 5 cm
Scale factor = 0.9
Therefore, the scale factor is 0.9.
How does the order matter when making rules for translations, rotations, reflections and dilations?
Select a point (neither the x-value or y-value may be 0).
Write down two different types of rules (translations, rotations, reflections and dilations) and perform them in one order. What is your final point?
Use the same original point and the same two rules but switch the order. What is your final point?
Show all of your steps.
The order of applying rules for translations, rotations, reflections, and dilations can affect the final outcome. Let's consider an example with an original point (2, 3).
First, let's perform a translation and then a rotation:
Translation: Move the point 3 units to the right and 4 units up.
(2, 3) -> (5, 7)
Rotation: Rotate the point 90 degrees counterclockwise about the origin.
(5, 7) -> (-7, 5)
Therefore, the final point after applying a translation followed by a rotation is (-7, 5).
Now, let's switch the order and perform a rotation followed by a translation:
Rotation: Rotate the point 90 degrees counterclockwise about the origin.
(2, 3) -> (-3, 2)
Translation: Move the point 3 units to the right and 4 units up.
(-3, 2) -> (0, 6)
Therefore, the final point after applying a rotation followed by a translation is (0, 6).
As we can see, the order of applying the rules yielded different final points.