Hello, I was wondering if I could get help on my unit test reveiw sheet. There are 4 problems, but the problems are still worth a great deal of my grade. If I could get help, with all or even a few, I will be thankful. The unit in geometry that I am focusing on is 'Similarity'.
Here they are:
1. It says Graph the Image of the figure after a dilation with the scale factor of 3/2 centered at (5,-5).
What would be the three coordinates of the dilation?
2. The length of angle CD is 9 units.
What is the length of the image of the line segment that after a dilation with a scale factor of 3/2? (Enter your answer in simplest form)
3. The larger triangle is the image of the smaller triangle after a dilation. The center of the dilation is (-2,-2).
What is the scale factor used to create the dilation?
4. Point J is located at (2,5) and point K is located at (4,19). What are the coordinates of the point that partitions the directed line segment JK in a 3:2 ratio?
+129657 ( 1) and (3) can't be answered without a figure shown.....!!!!
(2) 9 * (3/2) = 27/2 = 13.5 units long after dilation
4. Point J is located at (2,5) and point K is located at (4,19). What are the coordinates of the point that partitions the directed line segment JK in a 3:2 ratio?
The line is divided into 5 parts........the partition point will be located at 3/5 of the way between (2,5) and ( 4, 19) = [ 2 + (4 − 2)(3/5) , 5 + (19 − 5) (3/5) ] = [ 2 + 6/5 , 5 + 42/5] = [ 16/5 , 67/5]
Proof.....distance beween ( 2,5) and (4, 19) = √[ (4 − 2)^2 + ( 19 − 5)^2 ] = √ [ 4 + 196] = √200 = 10√2
Distance beween ( 2,5) and (16/5, 67,5) = √[ (16/5 − 2)^2 + ( 67/5 − 5)^2 ] =
√[ (6/5)^2 + ( 42/5 )^2 ] = √ [ 36 + 1764] / 5 = √1800 / 5 = 30√2 / 5 = 6√2
And 6√2 /10 √2 = 6 / 10 = 3/5
