Parallel and Perpendicular lines
A line, m, has slope 3. What is the slope of another line that is parallel to the line m?
3
True or False: A dilation with scale factor 1/2 will make the resulting image larger than the original image.
False
In SOH CAH TOA, SOH stands for:
sin = opposite/hypotenuse.
Write the corresponding equations for "CAH" and "TOA."
cosine = adjacent / hypotenuse
tangent = opposite / adjacent
A plane intersects a cylinder perpendicular to its base. Which two dimensional shape is formed by this cross section?
1) circle
2) rectangle
3) square
4) triangle
2) rectangle
Solve for x.
x + 2x = 180
x = 60
What is the negative reciprocal of 4/5 ?
-5/4
Point A is located at (4,-7). The point is reflected over the x axis. What are the coordinates of its image, A' ?
Hint: graph the point on your grid. Then reflect it over the x axis. What are the coordinates of the new point?
(4, 7)
Write down the pythagorean theorem
a2 + b2 = c2
The radius of a circle is 4. What is the exact area of the circle?
1) 4pi
2) 8pi
3) 16pi
4) 48
here is the formula for circumference of a circle
C = pi*2*r
Solve for r. That is, rewrite the equation so that it says
r =
Remember pi is a number!
r = C/(2*pi)
A line, m, has slope 5. What is the slope of a line that is perpendicular to line m?
-1/5
Which of the following transformation rules represents a dilation?
(a) (x,y) → (2x, 2y)
(b) (x,y) → (2x, 3y)
(c) (x,y) → (2x, y + 3)
(d) (x,y) → (x + 2, y + 3)
(a) (x,y) → (2x, 2y)
A triangle has angles 80 degrees and 75 degrees. What is the measure of the third angle?
25
The Volume of a pyramid is given by the formula
V= (1/3)B*h
where B is the area of the base and h is height of the pyramid.
Suppose a pyramid has a square base with side length 2. The height of the pyramid is 2. What is the volume of the pyramid?
V= (1/3) * 32 * 10
V= (1/3) * 9 * 2
V = 3 *2
V= 6
True or false: r2 = 2r
false,
r2 = r*r 2r is 2 multiplied by r.
another example:
42 = 4*4 not 4*2
A line, m, has slope 1/4. Which of the following lines is perpendicular to line m?
1) y = (1/4)x + 4
2) y = (-1/4)x + 3
3) y = 4x +8
4) y = -4x
4) y = -4x
A line reflection followed by a translation takes triangle ABC to triangle DEF.
Which statement is always true?
1) side BC is congruent to side EF
2) Side AC is congruent to side DE
3) Angle A is congruent to angle F
4) Angle B is congruent to Angle D
1) side BC is congruent to side EF
If two angles x and y sum to 90 degrees, then we know that sin(x) = cos(y). Based on this fact, sin(30) = cos of what angle?
1) 30
2) 60
3) 90
4) 100
2) 60
Write an equation of the line that is parallel to the line whose equation is 3y +? 7 = 2x and passes through the point (2,6).
First, rewrite 3y + 7 = 2x as y = _________.
Then, use point slope form:
y - y1 = m(x - x1)
3y + 7 = 2x
3y = 2x - 7
y = (2/3)x - 7/3, so my slope is 2/3
y - 6 = (2/3)(x - 2)
Here is the formula for volume of a cylinder.
V = pi*r2*h,
where h = height. If I know that the volume of the cylinder is 90pi and the radius is 3, which equation can I set up to solve for the height?
1) 3 = pi*32*h
2) 90 = pi*33*h
3) 90pi = pi*r2*3
4) 90pi = pi*32*h
4) 90pi = pi*32*h
Select the equation for a line that is parallel to
y = -2x +3, and passes through the point (4,1)
1) y - 4 = -2(x - 1)
2) y -1 = -2(x - 4)
3) y - 1 = 4(x + 4)
2) y - 1= -2(x - 4)
Which transformation would not carry a square onto itself?
(1) a reflection over one of its diagonals
(2) a 90 degree rotation clockwise about its center
(3) a 180 degree rotation about one of its vertices
(4) a reflection over the perpendicular bisector of one side
(3) a 180 degree rotation about one of its vertices
In triangle ABC, AB = 5, AC = 12, and angle A = 90 degrees. In triangle DEF, angle D = 90 degrees, DF = 12, and EF = 13.
Jessica says that triangle ABC is congruent to triangle DEF. Is she correct? Explain your answer.
You must draw the triangles in order to answer this correctly.Hint: Use pythagorean theorem to compute the lengths of the third side of each triangle.
Yes, Jessica is correct. We can use pythagorean theorem to get the 3rd sides of each triangle. Triangle ABC has hypotenuse 13, so its sides are 5,12,13. In triangle DEF, we know that the hypotenuse is 13. Therefore, the missing side has length 5. So its sides are also 5,12,13. By Side-Side-Side, the two triangles are congruent.
True or false: both of the following are valid formulas for the Circumference of a circle:
C = 2*r*pi
C = pi*d
where r is the radius and d is the diameter
True because d = 2r
3x + 4y = 9
Solve for y. write in the form y = mx + b
y = 9/4 -(3/4)x
or
y = (-3/4)x + (9/4)