What is the image of c for a 90 degree counterclockwise rotation about a?

counter clockwise would be rotating it up to the right.

C is 4 spaces away from A ,

 A is on X3 & Y3 so 4 +3 = 7

so it would be x7 & Y3 so (7,3), the first answer

Option A. (7, 3)

Step-by-step explanation:

When C is rotated 90° counterclockwise about the point A then C' will come parallel to the point A.

Now we can find the coordinates of the image of point C.

Distance between point A and C is 4 units, so x coordinates of C' (image) will be = 3 + 4 = 7

And y coordinates will remain as 3.

So the new image point C' will be (7, 3)

Option A. (7, 3) is the correct option.

1k

step-by-step explanation:

-6k+7k

(-6+7)k

1k

18 units²

step-by-step explanation:

first let's find altitude bd using the distance formula

d = √((y₂ - y₁)² + (x₂ - x₁)²)

bd = √((0 - -3)² + (0 - 3)²)

bd = √18

given the placement of points a and c, we can denote that point d bisects segment ac.

we will call ac the base.

using the distance formula

ac = √((0 - 6)² + (-6 - 0)²)

ac = √72

knowing our base and our height, we can plug these into our triangle area formula

area = (b * h)/2

area = (√18 * √72) / 2

area = (√1296) / 2

area = 36 / 2

area = 18 units²