Question

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translations in the coordinate plane. translate $\triangle abc$ 4 units up to form $\triangle abc$. where will the image of $\triangle abc$ be located? quadrant i quadrant ii quadrant iii quadrant iv

Explanation:

Step1: Identify original coordinates

First, find the coordinates of \( A \), \( B \), \( C \). From the graph:

• \( A(1, -2) \)
• \( B(4, -1) \)
• \( C(3, -3) \)

Step2: Apply translation (up 4 units)

Translating a point \((x, y)\) 4 units up means adding 4 to the \( y \)-coordinate: \((x, y + 4)\).

• For \( A(1, -2) \): \( (1, -2 + 4) = (1, 2) \)
• For \( B(4, -1) \): \( (4, -1 + 4) = (4, 3) \)
• For \( C(3, -3) \): \( (3, -3 + 4) = (3, 1) \)

Step3: Determine quadrant

All translated points \((1, 2)\), \((4, 3)\), \((3, 1)\) have positive \( x \) and positive \( y \) coordinates, which is Quadrant I.

Answer:

Quadrant I