Mathematics: What is the perimeter of rectangle that is 92 feet long and 46 feet wide?

What is the perimeter of rectangle that is 92 feet

ToonGamesToo

01.10.2021

Option B: y-3 is the correct option

Explanation:

The coordinates of the triangle ABC are A(-6,10), B(-7,7) and C(-4,6)

The co-ordinates of the image triangle A'B'C' are A'(2,7), B'(1,4) and C'(4,3)

To determine the translation rule, we can see from the figure that the image is translated right and down.

The translation is given by:

$(x+y) \rightarrow(x+k, y-c)$

We can see from Point A to A',

$A(-6,10) \rightarrow A^{\prime}(-6+8, 10-c)=A^{\prime}(2,7)$

To determine the value of c, we have,

$10-c=7\\$

-c=-3

c=3

Thus, from point B to B',

$B(-7,7) \rightarrow B^{\prime}(-7+8, 7-c)=A^{\prime}(1,4)$

Solving c, we have,

$\begin{aligned}7-c &=4 \\-c &=-3 \\c &=3\end{aligned}$

Also for point C to C',

$C(-4,6) \rightarrow C^{\prime}(-4+8, 6-c)=A^{\prime}(4,3)$

Solving for c, we have,

$\begin{aligned}6-c &=3 \\-c &=-3 \\c &=3\end{aligned}$

Thus, from all the above three points, the value of c is 3.

Hence, the translation is given by

$(x+y) \rightarrow(x+8, y-3)$

Hence, Option B is the correct answer.

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