Unit 1 Transformations
Figure ABCD in the coordinate plane has vertices at A(2, 4), B(2, 7), C(-3, 4), and D(-3, 7). Translate the figure 2 units right and 3 units down. What are the new points?
A(4,1) B(4,4) C(-1,1) D(-1,4)
Angle A and B are vertical angles. If angle A is 84 degrees, what is the measure of Angle B?
84 degrees
Factor the following quadratic:
y = 2x2 + 13x – 7
(x+7)(2x-1)
Simplify:
7√8 + 3√2
17√2
Do these sides make a triangle? If so, what kind?
6, 10, and 13
Yes, obtuse triangle.
Dilate the following points by a scale factor of 3: (1,2) and (3,4)
(3,6) and (9,12)
Angle A and B are alternate interior angles. Angle A = (8x-1) and Angle B = (11x-25). Solve for x.
x=8
Solve the following equation by factoring. Also find the y-intercept.
y=-3x2 – 27x – 42.
X-intercepts: x=-7 and x=-2
Y-intercept: (0,-42)
Simplify the following radical:
4√63
12√7
The legs of a right triangle are 8 and 10. Find the hypotenuse. Write answer in simple radical form
Hypotenuse = 2√41
Reflect the following points along the line x=1: (5,-6) and (3,-4)
(-3,-6) and (-1,-4)
Angle A and B are same side interior angles. Angle A = (5x+3) and Angle B = (9x-33). What is the measure of Angle B?
B = 102 degrees
What value for c would make this quadratic a perfect square trinomial?
y = x2 + 10x + c
c=25
Simplify:
√6 * 2√32
16√3
In a 30/60/90 degree triangle, the long side = 21. Find the short side and the hypotenuse.
Short side = 7√3
Hypotenuse = 14√3
Rotate the following points 540 degrees counter clockwise: (-2,-7) and (-5,-3)
(2,7) and (5,3)
Angle A, B, and C make a triangle. Angle A = (9x-8), Angle B = (x+10), and Angle C = (x+2). Solve for x.
x=16
Solve the following quadratic using quadratic formula:
y = x2 - 8x - 20
x = 10 and -2
Simplify:
(80x-8 y12) / (10x3 y5)2
(4y2) / (5x14)
You have a right triangle. The opposite side length is 14 feet and the adjacent side length is 17 feet. Find the angle of elevation.
39.47 degrees
Rotate 270 degrees about the origin counterclockwise and dilate the points by 2 using the center (0,-4):
(5,-2) and (4,2)
After rotation: (-2,-5) and (2,-4)
After dilation: (-4,-6) and (4,-4)
Triangle ABC is an equilateral triangle. Angle A = (8x-44). Solve for x.
x=13
Complete the square and solve:
x2 - 6x = 7
Must have factored form and solution in answer.
(x-3)^2 = 16
x = 7, -1
Solve the following:
4√(x + 2) = 24
x = 34
An airplane took off at a 20 degree angle of elevation. When the plane reaches an altitude of 30,000 feet, how far has it traveled diagonally in the air?
Round to the nearest whole number.
87,714 feet