Question

1 pointA triangle is dilated by a scale factor of 3 with thecenter of dilation at the origin. Which statement istrue?1) The area of the image is nine times the area ofthe original triangle.2) The perimeter of the image is nine times theperimeter of the original triangle.3) The slope of any side of the image is threetimes the slope of the corresponding side of theoriginal triangle.4) The measure of each angle in the image is threetimes the measure of the corresponding angleof the original triangle.

Answer 1

We have two triangles. One is the dilated image, with a scale factor of 3, of the other triangle.

The angles of the dilated triangles stay the same, that is, they have the same measure.

The sides increase their length by a factor of 3.

Then, if we calculate the area, we will have:

`A_2=(b_2h_2)/(2)=((3b_1)(3h_1))/(2)=9(b_1h_1)/(2)=9A_1`

Then, the area of the dilated triangle is 3^2=9 times the are of the pre-image triangle.

Answer: 1) The area of the image is nine times the area of the original triangle.