Question

what will the coordinates of triangle rst be after it is translated 4 units down and 3 units left? graph of triangle rst on a coordinate grid options: \\( r(-1, -2), s(8, -1), t(5, -9) \\); \\( r(-7, -2), s(8, -1), t(-1, -1) \\); \\( r(-7, -2), s(2, -1), t(-1, -9) \\); \\( r(-1, 6), s(8, 7), t(5, -1) \\)

Explanation:

Step1: Find original coordinates

From the graph, we identify the original coordinates:

• \( R(-4, 2) \)
• \( S(5, 3) \)
• \( T(2, -5) \)

Step2: Apply translation rules

A translation of 4 units down means subtracting 4 from the \( y \)-coordinate, and 3 units left means subtracting 3 from the \( x \)-coordinate. The translation rule is \((x, y) \to (x - 3, y - 4)\).

For point \( R(-4, 2) \):

\( x \)-coordinate: \(-4 - 3 = -7\)
\( y \)-coordinate: \(2 - 4 = -2\)
So, \( R'(-7, -2) \)

For point \( S(5, 3) \):

\( x \)-coordinate: \(5 - 3 = 2\)
\( y \)-coordinate: \(3 - 4 = -1\)
So, \( S'(2, -1) \)

For point \( T(2, -5) \):

\( x \)-coordinate: \(2 - 3 = -1\)
\( y \)-coordinate: \(-5 - 4 = -9\)
So, \( T'(-1, -9) \)

Answer:

\( R(-7, -2) \), \( S(2, -1) \), \( T(-1, -9) \) (corresponding to the option \( R(-7, -2), S(2, -1), T(-1, -9) \))