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A triangle has the coordinates of [tex]\( A(-15, -3) \)[/tex], [tex]\( B(1, 1) \)[/tex], and [tex]\( C(9, -7) \)[/tex]. If the triangle is translated right 10 units and up 9 units, what are the new coordinates for point [tex]\( C \)[/tex]?

A. [tex]\((21, 8)\)[/tex]

B. [tex]\((19, 2)\)[/tex]

C. [tex]\((15, -2)\)[/tex]

D. [tex]\((28, -7)\)[/tex]



Answer :

GinnyAnswer
To solve this problem, we need to translate point [tex]\( C \)[/tex] by 10 units to the right and 9 units up. Let's break down the steps carefully:

1. Identify the Original Coordinates of Point [tex]\( C \)[/tex]:
The original coordinates of point [tex]\( C \)[/tex] are [tex]\((9, -7)\)[/tex].

2. Translate Right 10 Units:
- To move a point to the right, add the given units to the x-coordinate.
- Starting from [tex]\( x = 9 \)[/tex], add 10 units:
[tex]\[ 9 + 10 = 19 \][/tex]

3. Translate Up 9 Units:
- To move a point up, add the given units to the y-coordinate.
- Starting from [tex]\( y = -7 \)[/tex], add 9 units:
[tex]\[ -7 + 9 = 2 \][/tex]

4. Combine the New Coordinates:
- After translating right by 10 units and up by 9 units, the new coordinates for point [tex]\( C \)[/tex] are [tex]\((19, 2)\)[/tex].

Therefore, the new coordinates for point [tex]\( C \)[/tex] after the translation are:
\[
\boxed{(19, 2)}

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