The green triangle is a dilation of the red triangle with a scale factor of s=13 and the center of dilation is at the point (4,2)

What are the coordinates of Point C'? C'(___,____)

What are the coordinates of Point A? A(____,_____)

Answers:

================================================================

Explanation:

I'm assuming you mean to say "scale factor of s = 1/3" since the green triangle is smaller than the red triangle.

Let's start at the point (4,2). This is the center of dilation. This fixed point does not move or change as you apply any dilation (as long as you keep this as the center of course). Every other point will move. For instance, the point (10,14) moves to (6,6) after applying the dilation.

----------------------

The x coordinate of the center point (4,2) is x = 4.

The x coordinate of the point (10,14) is x = 10.

Going from (4,2) to (10,14) will have us move a horizontal distance of 10-4 = 6 units.

Take 1/3 of this horizontal distance and we get (1/3)*6 = 2. This means that if we started at the center point (4,2) and move 2 units to the right, we will have the x coordinate to be x = 4+2 = 6, which matches up with the x coordinate of the point (6,6)

-------------------------

We'll do the same sort of thing with the y coordinates

The point (4,2) has the y coordinate y = 2

The point (10,14) has the y coordinate y = 14

The vertical distance between those points is 14-2 = 12 units

One third of this is (1/3)*12 = 4

If we started at (4,2) and moved up 4 units, then the y coordinate goes from y = 2 to y = 2+4 = 6. This also matches (6,6)

----------------------------

Hopefully by now you have a sense of how this all works. Let's use these tricks to find the location of point A.

The horizontal distance from (4,2) to (8,4) is 8-4 = 4 units. This triples to 4*3 = 12 units. We triple here because we're going in reverse of the process described in the previous two sections. If (8,4) and A swapped places, then we would take one third instead.

We'll use that 12 to count out 12 horizontal spaces from (4,2) to get to (16,2). I added 12 to the x coordinate of (4,2).

Repeat the process for the y values. The vertical distance from (4,2) to (8,4) is 2 units, which triples to 6. Add 6 onto the y coordinate of (16,2) and we arrive at (16, 8) which is the location of point A.

--------------------------------

Now let's find the location of point C'

The horizontal distance from (-2,11) to (4,2) is 6 units because |-2-4| = 6. Multiply this by 1/3 and we get (1/3)*6 = 2

To get to the location point C', we need to start at (4,2) and move to the left 2 units. That means (4,2) will move to (2,2) as a temporary location.

We apply the same idea for the y coordinates. The vertical distance from (4,2) to (-2,11) is 9 units. This leads to (1/3)*9 = 3 units being the vertical distance from (4,2) to the location of C'. We'll add 3 to the y coordinate of (2,2) to arrive at (2,5) which is the location of C'.

I need help with this question

.Evaluate (103)^3using identity.​

game item?? game name???

The ratio 2 centimetres to 5 metres can be written in the form
1
:
n
.

Find the value of
n
.

8. Solve for x. Round to the nearest hundredth If necessary.

what is 5x-2y= -4 in slope intercept form

The cost of 25 litres of petrol is Rs.1400.Find the cost of 30 litres of petrol.​

What is the gcf of 10m^3 +45m

Help????? 5 rate its due at 8:00 hehee.....

school lunches cost ₱35.50 per week. about how much would 15.5 weeks of lunches cost?grade v​

What is an equation of the line that passes through the points (4, -6) and
(8,-4)?

The solution (x y) to a system of equatiohs is the point where they..?

What is the area of a triangle whose base measures 3.2 centimeters and whose height is 4.6 centimeters.

What is the range for the function below?

The probability that Stu buys a sandwich is 0.5. The probability that Stu gets the bus is 0.8. Assuming the events are independent, what is the probability that Stu buys a sandwich and gets the bus?

Solve for the hypotenuse in the right triangle shown.​

Help pleaseeeeit won’t let me send it cuz it has to be longer soo...

Find the area of the sector.
45 degrees
11 cm radius

Hi, can someone please help me with some geometry problems?!!!

What are the coordinates of point S?

There are 90 penguins in a zoo. There are two types - Humboldt and Emperor.
52 are female, of these 6 are Emperor penguins.
There are 5 male Emperor penguins.
Use this information to complete the frequency tree.
PLEASE ANSWER I WILL GIVE BRAINLIEST!!!

Alguien me podría ayudar aunque sea en la 2°
se los agradecería mucho​

Peter picks one bill at a time from a bag and replaces it. He repeats this process 100 times and records the results in the table.

Based on the table, which bill has an experimental probability of being drawn from the bag next?

Experimental or Theoretical?

What is the equation of a horizontal line passing through the point (−7, 5)? (1 point)

y = 5
y = −7
x = 5
x = −7

find the area of the figure below, composed of a rectangle and semicircle. Round it to the nearest tenth.

Pasha traveled 217 miles in 3.5 hours, how far does she travel in 1 hour

If BE = 2x + 2, BD = 5× - 3, and AE = 4× - 6, what are the values of x and AC?​

What is the measure of the indicated angle?

Solve the equation r+3 = 3(r-5)​

Help please I forgot how to do this