Question

A triangle with vertices (0,0), (5,3), (10,1) is dilated at the origin factor of 5. What are the new vertices?

Answer 1

Answer: $(0,0)$, $(25,15)$, $(50,5)$

Step-by-step explanation:

A dilation is defined as a transformation in which the image has the same shape as the pre-image, but they have different sizes.

You know that the triangle given in the exercise is dilated at the origin and the scale factor is 5.

Then, in order to find the new vertices, you must multiply the coordinates of each  original vertex by the scale factor 5:

$(x,y)$→$(5x,5y)$

Therefore, applying this procedure, you get that the new vertices are:

$(5*0,\ 5*0)$ → $(0,0)$

$(5*5,\ 5*3)$ → $(25,15)$

 $(5*10,\ 5*1)$ → $(50,5)$

Answer 2

Answer:

see explanation

Step-by-step explanation:

Since the dilatation is centred at the origin then the image is 5 times the original coordinates, that is

(0, 0 ) → (5 × 0, 5 × 0 ) → (0, 0 )

(5, 3 ) → (5 × 5, 3 × 5 ) → (25, 15 )

(10, 1 ) → (10 × 5, 1 × 5 ) → (50, 5 )