Question
Trapezoid JKLM is shown on the coordinate plane.
Trapezoid JKLM on the coordinate plane with ordered pairs at J negative 2, 1, at K 1, 1, at L 3, negative 2, at M negative 4, negative 2.
If trapezoid JKLM is translated using the rule (x, y) → (x + 3, y − 3) and then translated using the rule (x, y) → (x + 2, y − 2) to create trapezoid J″K″L″M″, what is the location of K″?
(4, 6)
(6, −4)
(8, −7)
(7, −8)
Answers
GPT-4o mini
To find the location of point \( K'' \) after performing the translations on trapezoid \( JKLM \), we'll start by determining the original coordinates of point \( K \), which is given as \( K(1, 1) \).
1. **First Translation**: The rule for the first translation is \((x, y) \rightarrow (x + 3, y - 3)\).
- Applying this to point \( K(1, 1) \):
\[
K' = (1 + 3, 1 - 3) = (4, -2)
\]
2. **Second Translation**: The rule for the second translation is \((x, y) \rightarrow (x + 2, y - 2)\).
- Now applying this to point \( K'(4, -2) \):
\[
K'' = (4 + 2, -2 - 2) = (6, -4)
\]
Thus, the coordinates of point \( K'' \) after both translations is \( (6, -4) \).
The answer is \( (6, -4) \).
1. **First Translation**: The rule for the first translation is \((x, y) \rightarrow (x + 3, y - 3)\).
- Applying this to point \( K(1, 1) \):
\[
K' = (1 + 3, 1 - 3) = (4, -2)
\]
2. **Second Translation**: The rule for the second translation is \((x, y) \rightarrow (x + 2, y - 2)\).
- Now applying this to point \( K'(4, -2) \):
\[
K'' = (4 + 2, -2 - 2) = (6, -4)
\]
Thus, the coordinates of point \( K'' \) after both translations is \( (6, -4) \).
The answer is \( (6, -4) \).