Answer and Explanation:
Triangles (1-2)
We can identify two right triangles with the angle measures:
• 30-60-90
• 20-70-90
From this information, we can form the following equations with x and y using the Angle Addition Postulate:
x + 20 = 30
x = 10
y + 30 = 70
y = 40
Slopes (3-5)
We can find the slope of each line using the formula:
slope = rise / run
So, the slopes of the three lines are (in order of increasing y-intercept):
1 / 5 = 1/5
2 / 1 = 2
1 / 1 = 1
Translations (6-7)
We can see that EFGH is twice as large as ABCD, so we can start with a 2 times dilation from point A. Then, we can reflect the shape over the center of the graph to get to EFGH.
Dilated Point (8)
When we are asked to dilated a point from the origin, we can multiply each coordinate by the scale factor to get the resulting point.
(-9 × 1.5, 3.4 × 1.5)
(-13.5, 5.1)
Hanger (9-10)
Representing the weight each triangle as x and each square as y, we can construct the following equation, assuming that both sides of the hanger are equal weight:
x + 3y = 4x + y
Notice that there is 1 triangle (x) and 3 squares (y) on the right, and there are 4 triangles (x) and 1 square (y) on the left.
If we plug 6 in for x, we can solve for y using algebraic manipulation:
6 + 3y = 4(6) + y
↓ subtracting y from both sides
6 + 2y = 24
↓ subtracting 6 from both sides
2y = 18
↓ dividing both sides by 2
y = 9