Scaled Copies & Dilations
In a scaled copy, every length is multiplied by this one number called what?
A scale factor
If you dilate a figure by a scale factor of 7, will it get larger or smaller?
Larger
The three angles in any triangle adds up to how many degrees?
180!!
Another way to say the slope is the ___/____
Rise/Run
What is the general equation of a line?
y=mx+b
A 4 by 6 rectangle is dilated into a 6 by 9 rectangle. What is the scale factor?
1.5 or 3/2
A dilation with center (0,0) and scale factor 3 sends (2,1) to what point?
(6,3)
Triangle P has angles 40 and 70 degrees. Triangle Q has angles 70 and 70 degrees. Are they similar?
Yes, P's third angle is 70 degrees. Q's third angle is 40 degrees.
Which line is steeper: slope 5/8 or slope 2/3?
Slope 2/3 is steeper
If a line has a slope of 2 and a y-intercept of -3; what is the equation of this line?
y=2x-3
In a dilation, this is the point you use to dilate a figure.
the center of dilation
If you dilate a triangle with angles (30, 60, 90 degrees) by a scale factor of 3, what will the angles of the dilated figure be?
30, 60, 90
Similar polygons have corresponding angles that are _______ and corresponding sides that are ________.
Congruent; proportional
Slope is found by dividing this change by this change.
the change is y divided by the change in x
A line cross the y-axis at (0,0) and has a slope of 2, what is the equation of that line?
y=2x
15cm
A dilation with center (0,0) and scale factor is 1/2 would send (8,-2) to what point?
(4,-2)
A 3 by 8 rectangle and a 6 by 12 rectangle both have four right angles. Are they similar?
No. The sides are not proportional. 6/3=2; 12/8=1.5
2
What is the point-slope equation of a line?
y2 - y1 = m(x2 - x1)
A dilation with a scale factor 2 sends A to A' they are 12cm apart. How far is the center from A?
A dilation with center (0,0) and scale factor 2 sends P to (10, -6). What was the original coordinate?
(5,-3)
Figure F is reflected, then dilated with a scale factor 3. In F, one side is 4cm and one angle is 65 degrees. What are the matching side and angle in the final image?
65 degrees & 12cm
A line has slope 3/2 and passes through (2,1). Which point is also on that line: (6,7), (6,6) or (4,3)
(6,7)
Write the equation of the line that goes through the points (10,10) and (2,6)?
y=0.5x+5