Question

the figure shows a triangle on a coordinate plane.
which of the following shows the triangle translated 3 units to the left and 2 units down?
a
b
c
d

Explanation:

Step1: Recall translation rules

For a point \((x,y)\) in a coordinate plane, translating 3 units left means subtracting 3 from the \(x\)-coordinate, and translating 2 units down means subtracting 2 from the \(y\)-coordinate. So the transformation is \((x,y)\to(x - 3,y - 2)\).

Step2: Analyze the original triangle's position

Assume the original triangle has a vertex (for simplicity, take the top vertex) at, say, \((2,2)\) (from the grid). After translation: \(x=2 - 3=- 1\), \(y = 2-2 = 0\). Now check the options:

• Option A: The triangle is moved right and up, not left and down.
• Option B: Let's check the coordinates. If we take a vertex of the original triangle (e.g., if original is around \((2,2)\)), after moving 3 left (\(2-3=-1\)) and 2 down (\(2 - 2=0\)), the position in option B matches this translation (left and down).
• Option C: The triangle is moved down but not enough left (or wrong direction in \(x\)).
• Option D: The triangle is moved right, not left.

Answer:

B