Question

in the standard (x, y) coordinate plane, a triangle has vertices (-3, -3), (-4, 2), and (-1, 1). what will be the coordinates of...
options:
a (-3, -5), (-4, 4), and (-1, 3)
b (-6, -3), (-4, 4), and (-1, 3)
c (-3, -5), (-4, 0), and (-1, -1)
d (-3, -1), (4, -4), and (3, 1)
e (-5, 3), (0, -4), and (-1, -1)

Explanation:

Step1: Analyze the problem type

This is a coordinate transformation problem for a triangle's vertices. We need to determine the correct new coordinates after some transformation (likely a translation or reflection, but since the original vertices are (-3, -3), (-4, 2), (-1, 1), we can check the differences between original and each option.

Step2: Check Option C

Original vertices: \((-3, -3)\), \((-4, 2)\), \((-1, 1)\)
For Option C: \((-3, -5)\), \((-4, 0)\), \((-1, -1)\)
Calculate the change in y - coordinates:

• For \((-3, -3)\) to \((-3, -5)\): \(-5 - (-3)= - 2\)
• For \((-4, 2)\) to \((-4, 0)\): \(0 - 2=-2\)
• For \((-1, 1)\) to \((-1, -1)\): \(-1 - 1=-2\)

So there is a vertical translation of - 2 (down 2 units) for all y - coordinates, which is consistent. Let's check other options:

• Option A: y - changes are \( - 5-(-3)=-2\), \(4 - 2 = 2\) (inconsistent)
• Option B: x - change for first vertex: \(-6-(-3)=-3\), inconsistent with others.
• Option D: x and y changes are inconsistent (e.g., from (-3, -3) to (-3, -1): y change + 2, but from (-4, 2) to (4, -4): x and y changes are large and inconsistent)
• Option E: All coordinates are inconsistent with a simple transformation.

Answer:

C. \((-3, -5)\), \((-4, 0)\), and \((-1, -1)\)