Question

draw the following triangle after a translation 1 unit to the left and 3 units up.

Explanation:

Step1: Identify original vertices

First, find the coordinates of the original triangle's vertices. From the graph, let's assume the vertices are \( A(-3, 4) \), \( B(-4, 2) \), \( C(3, -4) \) (we can determine these by looking at the grid intersections).

Step2: Apply translation rules

For a translation 1 unit left (subtract 1 from \( x \)-coordinate) and 3 units up (add 3 to \( y \)-coordinate):

• For vertex \( A(-3, 4) \):

New \( x \): \( -3 - 1 = -4 \)
New \( y \): \( 4 + 3 = 7 \)
So new \( A'(-4, 7) \)

• For vertex \( B(-4, 2) \):

New \( x \): \( -4 - 1 = -5 \)
New \( y \): \( 2 + 3 = 5 \)
So new \( B'(-5, 5) \)

• For vertex \( C(3, -4) \):

New \( x \): \( 3 - 1 = 2 \)
New \( y \): \( -4 + 3 = -1 \)
So new \( C'(2, -1) \)

Step3: Draw the new triangle

Plot the new vertices \( A'(-4, 7) \), \( B'(-5, 5) \), \( C'(2, -1) \) on the grid and connect them to form the translated triangle.

Answer:

The translated triangle has vertices at \((-4, 7)\), \((-5, 5)\), and \((2, -1)\). (To draw, plot these points and connect them.)