What is the image of (-9, 2) after a dilation by a scale factor of 3 centered at the
origin?

The image of the point is (-27, 6)

Step-by-step explanation:

Let us talk about the dilation

∵ Point (-9, 2) is dilated by a scale factor 3

∴ k = 3

∵ The center of dilation is the origin

→ Multiply the coordinates of the point by 3 to find the image

∴ The image = (3 × -9, 3 × 2)

∴ The image = (-27, 6)

The image of the point is (-27, 6)

something that characterises a right triangle is the fact that we may use pythagoras' theorem to find any one of its sides given that we have the length of the other two sides. here, we have the length of the hypotenuse, √(87) yd, and one other side, √(23) yd, thus we can easily find the length of the remaining side using pythagoras' theorem as defined below:

c^2 = a^2 + b^2, where c is the length of the hypotenuse, and a and b are the lengths of the other two sides.

thus, given that c = √(87) and a = √(23), we may substitute these into the formula we defined above to get:

c^2 = a^2 + b^2

(√87)^2 = (√23)^2 + b^2 (substitute c = √87 and a = √23 into the equation)

87 = 23 + b^2 (evaluate (√87)^2 = 87 and (√23)^2 = 23 - remember that the square root of a number, squared will equal that very same number)

64 = b^2 (subtract 23 from both sides)

√64 = b (take the square root of both sides)

8 = b (evaluate √64 = 8)

therefor, the length of the unknown leg in the right triangle is 8 yd (first answer).

i am sorry it just submitted an answer but the answer is 365 boys. hopes this

step-by-step explanation: