A playground has a fence covering an area with the coordinates of A(2, 3), B(-3, 2), and C(2, -2). The park wants to extend the fence’s range by a scale factor of 2. What are the new points? A’ B’ C’
Does this enlarge or shrink the shape? (Circle the correct answer.)

Answers:

A ' (4,6)

B ' (-6,4)

C ' (4,-4)

The shape is enlarged

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Explanation:

The scale factor of 2 means we'll multiply each coordinate, of each point, by this value. Something like A(2,3) becomes A'(4,6) after doubling the coordinates. The same applies with points B and C as well.

Since each coordinate doubles, the point moves further away from the origin (0,0). This means the overall image is larger compared to its preimage. Therefore, we have an enlargement.

The shape only shrinks if the scale factor is between 0 and 1, excluding both endpoints. For example, a scale factor of 0.5 means each side is half as long as before.

The graph is shown below.

the system of inequity is

step-by-step explanation:

from the given graph it is noticed that we have two related lines. one is solid and another is dashed.

if a line passing through two points, then the equation of line is

the solid line passing through the points (0,4) and (4,0).

the related equation of solid line is .

similarly, find the related equation of dashed line. the dashed liune passing through the points (0,0) and (3,1).

the related equation of dashed line is

from the given graph it is noticed that the point (0,1) lies on the shaded region, therefore the point (0,1) must be satisfied by the related equations.

check the related equations by the point (0,1).

this statement is true if the sign of inequality is < instead of equality. since it is an solid line therefore the sign of inequality will be . the required inequality is

similarly, check the second related equation.

it is a dashed line, so this statement is true if the sign of inequality is > . the required inequality is