Unit 1 Transformations
Figure ABCD in the coordinate plane has vertices at (2, 4), (2, 7), (-3, 4), and (-3, 7). Translate the figure 2 units right and 3 units down. What are the new points?
(4,1) (4,4) (-1,1) (-1,4)
Angle A and B are vertical angles. If angle A is 84 degrees, what is the measure of Angle B?
84 degrees
Find the √-25 ?
5i
Graph the following equation: y=-3x2 – 24x – 42.
Find the vertex and the y-intercept.
Vertex: (-4,6)
Y-intercept: (0,-42)
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 same side interior angles. If angle A is 73 degrees, what is the measure of Angle B?
107 degrees
Simplify the following radical:
√63
3√7
Factor the following quadratic:
y = 2x2 + 13x – 7
(x+7)(2x-1)
The legs of a right triangle are 6 and 8. Find the hypotenuse.
Hypotenuse = 10
Reflect the following points along the x-axis: (5,-6) and (3,-4)
(5,6) and (3,4)
Angle A and B are alternate interior angles. Angle A = (8x-1) and Angle B = (11x-25). Solve for x.
x=8
Simplify:
7√5 + 3√5
10√5
Solve the following quadratic using quadratic formula:
y = x2 -8x -20
x = 10 and -2
The angle of elevation of a right triangle is 24 degrees. The hypotenuse is 13 inches long. Find the length of the adjacent side. Round to the hundredths place.
11.88 inches
Rotate the following points 180 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
3Simplify:
(80x6 y2) / (10x3 y5)
8x3 / y3
Find the value of c that will complete the square:
y = x2 + 10x + c
c = 25
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. Round to the hundredths place.
39.47 degrees
Translate the following points left 3 and up 1 AND THEN rotate 270 degrees about the origin counterclockwise: (5,-2) and (4,2)
After translation: (2,-1) and (1,3)
After rotation: (-1,-2) and (3,-1)
Triangle ABC is an equilateral triangle. Angle A = (8x-44). Solve for x.
x=13
Solve the following:
4√(x + 2) = 24
x = 34
Complete the square and solve:
x^2 - 6x = 7
Must have factored form and solution in answer.
(x-3)2 = 16
x = 7, -1
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