Describe a dilation (center and scale factor) that transformation triangle rst into triangle r’s’t’ or explain why it cannot be done

We need to see the triangles - I am assuming you have some problem on a sheet. However if you're just talking about any dilation -

How to Dilate a Triangle:

Choose any point on a x,y grid, mark the distance between that point and the points of the triangle.

You can now 'dilate' that triangle by multiplying all the distances by the scale factor.

Example:

Let's say our scale factor is 0.5

We'll use the origin as the point for our dilation. If the distance from the origin to R is 4 c.m. we then multiply it by our scale factor (0.5) to get 2 c.m.

Now we mark R' at 2 c.m. and repeat the process for all points

The full question on my assignment goes like this:

a. Describe a dilation (center and scale factor) that transforms triangle RST into triangle R'S'T' or explain why it cannot be done.

b. In either case, use complete sentences to describe the relationship that exists between the corresponding sides and angles.

My answers:

a.

The center of the dilation is the origin. The scale factor is 3.  

b.

The relationship that exists between the corresponding sides and angles is that the corresponding sides have the same ratio and the corresponding angles have the same ratio, too.

I had this problem on my assignment, so I know what triangles you are talking about.

Triangle RST has coordinates of:

(1, 1) S

(2, 1) T

(1, 2) R

Triangle R'S'T' has coordinates of:

(3, 3) S'

(6, 3) T'

(3, 6) R'

Hope this helps!

c

step-by-step explanation:

step-by-step explanation:

equation

you are asked to write the equation

  expression = 0

using the given expression. when you do that, you have

  2x^2-2x-12 = 0

factoring

you can see that each of the coefficients is even, so a factor of 2 can be removed immediately.

  2(x^2 -x -6) = 0

if you multiply the binomials (x+a)(x+b), you get

  (x +a)(x +b) = x^2 +(a+b)x +ab

this tells you the coefficient of x is the sum of two factors of the constant term. here, that means -1 is the sum of two factors of -6. we want to know those factors so we can factor the trinomial.

  -6 = -1×6 = -2×3 = -3×2 = -6×1

the factor pair that sums to -1 is {-3, 2}, so our factorization is

  2(x -3)(x +2) = 0

solutions

the solutions to this equation are the values of x that make the product zero. a product is zero only when only of the factors of the product is zero. here, that means

  x - 3 = 0

  x = 3 . . . add 3 to both sides of the equation

or

  x +2 = 0

  x = -2 . . . add -2 to both sides of the equation

the solutions to the equation are x=3 or x=-2. both of these values of x satisfy the equation—they make it be true.