Question

translate the figure 2 units right and 2 units up.
draw a vector from the origin 2 units right and 2 units up.

Explanation:

Step1: Identify original vertices

First, find the coordinates of the original triangle's vertices. From the graph, the left vertex is at \((-7, -1)\), the top - right vertex is at \((-4, -1)\), and the bottom vertex is at \((-4, -7)\).

Step2: Apply translation rule

To translate a point \((x,y)\) 2 units right and 2 units up, we use the transformation \((x + 2,y + 2)\).

• For the point \((-7,-1)\):

New \(x\) - coordinate: \(-7+2=-5\)
New \(y\) - coordinate: \(-1 + 2=1\)
So the new point is \((-5,1)\)

• For the point \((-4,-1)\):

New \(x\) - coordinate: \(-4+2=-2\)
New \(y\) - coordinate: \(-1 + 2=1\)
So the new point is \((-2,1)\)

• For the point \((-4,-7)\):

New \(x\) - coordinate: \(-4+2=-2\)
New \(y\) - coordinate: \(-7 + 2=-5\)
So the new point is \((-2,-5)\)

Step3: Draw the translated figure

Plot the points \((-5,1)\), \((-2,1)\) and \((-2,-5)\) on the coordinate plane and connect them to get the translated triangle.

For the vector: The vector from the origin \((0,0)\) 2 units right and 2 units up has its terminal point at \((2,2)\). We draw a line segment from \((0,0)\) to \((2,2)\) with an arrow at \((2,2)\) to represent the vector.

Answer:

The translated triangle has vertices at \((-5,1)\), \((-2,1)\), \((-2,-5)\) and the vector has its terminal point at \((2,2)\) (the vector is drawn from \((0,0)\) to \((2,2)\)).