Triangle abc with vertices a(2, 4) , b(4, 0) , and c(6, 6) is dilated about the origin to be triangle a′b′c′ .

Triangle ABC is dilated by a scale factor of 1.5

Step-by-step explanation:

The general rule for the dilation about the origin with a factor of k is

You are given two triangles ABC and A'B'C'.

In triangle ABC:

From the diagram, in triangle A'B'C':

As you can see

So, triangle ABC is dilated by a scale factor of

Step-by-step explanation:

Givens

According to the graph, the vertices of the dilated triangle are A'(3,6), B'(6,0) and C'(9,9).

Notice that the dilation factor is a quotient between a dilated coordinate and an original coordinate. If we do this division

Therefore, the dilation factor is 1.5.

The right answer is the second choice.

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step-by-step explanation:

{x = -1/2 ,   y = -1

step-by-step explanation:

solve the following system:

{2 x + y = -2

{10 x - 3 y = -2

in the first equation, look to solve for y:

{2 x + y = -2

{10 x - 3 y = -2

subtract 2 x from both sides:

{y = -2 x - 2

{10 x - 3 y = -2

substitute y = -2 x - 2 into the second equation:

{y = -2 x - 2

{10 x - 3 (-2 x - 2) = -2

10 x - 3 (-2 x - 2) = (6 x + 6) + 10 x = 16 x + 6:

{y = -2 x - 2

{16 x + 6 = -2

in the second equation, look to solve for x:

{y = -2 x - 2

{16 x + 6 = -2

subtract 6 from both sides:

{y = -2 x - 2

{16 x = -8

divide both sides by 16:

{y = -2 x - 2

{x = -1/2

substitute x = -1/2 into the first equation:

{y = -1

{x = -1/2

collect results in alphabetical order:

answer:   {x = -1/2 ,   y = -1