Question

translate the figure 2 units right and 1 unit down. plot all of the points of the translated figure. you may click a plotted point to delete it.

Answer:

To solve the translation of the figure, we first identify the coordinates of the original vertices. Let's assume the original points (from the graph) are:

• Point 1: \((-5, -1)\)
• Point 2: \((-5, -4)\)
• Point 3: \((-8, -7)\)
• Point 4: \((-4, -8)\) (Wait, actually, looking at the triangle, let's re - identify the original vertices correctly. From the graph, the three vertices of the triangle seem to be:
• Vertex A: \((-5, -1)\)
• Vertex B: \((-5, -4)\)
• Vertex C: \((-8, -7)\)
• Vertex D: \((-4, -8)\)? No, it's a triangle, so three vertices. Let's check again. The vertical line from \((-5, -1)\) to \((-5, -4)\), then a point at \((-8, -7)\) and \((-4, -8)\)? Wait, maybe the three vertices are \((-5, -1)\), \((-5, -4)\), and \((-8, -7)\) and \((-4, -8)\) is a mistake. Let's take the three vertices as:
• \(A(-5, -1)\)
• \(B(-5, -4)\)
• \(C(-8, -7)\)
• \(D(-4, -8)\) is incorrect. Wait, the figure is a triangle, so three points. Let's look at the grid. The top point is \((-5, -1)\), then down to \((-5, -4)\), then to the left - down \((-8, -7)\) and right - down \((-4, -8)\)? No, maybe it's a triangle with vertices \((-5, -1)\), \((-5, -4)\), and \((-8, -7)\) and \((-4, -8)\) is a typo. Let's proceed with the translation rule: for a translation of \(h\) units right and \(k\) units down, the new coordinates \((x', y')=(x + h,y - k)\), where \(h = 2\) and \(k = 1\).

Step 1: Translate Vertex \(A(-5, -1)\)

For a translation 2 units right (\(x\) - coordinate increases by 2) and 1 unit down (\(y\) - coordinate decreases by 1).
The formula for translation is \((x,y)\to(x + 2,y-1)\).
For \(A(-5, -1)\):
\(x'=-5 + 2=-3\)
\(y'=-1-1=-2\)
So the translated point \(A'(-3, -2)\).

Step 2: Translate Vertex \(B(-5, -4)\)

Using the same translation rule \((x,y)\to(x + 2,y - 1)\).
\(x'=-5 + 2=-3\)
\(y'=-4-1=-5\)
So the translated point \(B'(-3, -5)\).

Step 3: Translate Vertex \(C(-8, -7)\)

Applying the translation:
\(x'=-8 + 2=-6\)
\(y'=-7-1=-8\)
So the translated point \(C'(-6, -8)\).

Step 4: Translate Vertex \(D(-4, -8)\) (if it's a vertex)

\(x'=-4 + 2=-2\)
\(y'=-8-1=-9\)
Wait, but if it's a triangle, maybe the three vertices are \((-5, -1)\), \((-5, -4)\), and \((-8, -7)\) and \((-4, -8)\) is the fourth? No, the original figure is a triangle, so let's correct the original vertices. Let's assume the three vertices are:

• \(A(-5, -1)\)
• \(B(-5, -4)\)
• \(C(-8, -7)\)
• \(D(-4, -8)\) is wrong. Let's look at the graph again. The vertical segment is from \((-5, -1)\) to \((-5, -4)\), then a segment to \((-8, -7)\) and a segment to \((-4, -8)\). So it's a quadrilateral? Maybe. Let's proceed with all four points.

For point \((-5, -1)\):
New \(x=-5 + 2=-3\), new \(y=-1-1=-2\) → \((-3, -2)\)

For point \((-5, -4)\):
New \(x=-5 + 2=-3\), new \(y=-4-1=-5\) → \((-3, -5)\)

For point \((-8, -7)\):
New \(x=-8 + 2=-6\), new \(y=-7-1=-8\) → \((-6, -8)\)

For point \((-4, -8)\):
New \(x=-4 + 2=-2\), new \(y=-8-1=-9\) → \((-2, -9)\)

To plot the translated figure, we plot the points \((-3, -2)\), \((-3, -5)\), \((-6, -8)\), and \((-2, -9)\) (if it's a quadrilateral) or the three points if it's a triangle (maybe I misidentified the original figure). But following the translation rule \( (x,y)\to(x + 2,y - 1) \), we can find the new coordinates of each original vertex and plot them.

If we consider the original triangle with vertices \((-5, -1)\), \((-5, -4)\), and \((-8, -7)\) and \((-4, -8)\) is an error, and it's a triangle with three vertices:

• Original vertex 1: \((-5, -1)\) → Translated: \((-5 + 2, -1-1)=(-3, -2)\)
• Original vertex 2: \((-5, -4)\) → Translated: \((-5 + 2, -4 - 1)=(-3, -5)\)
• Original vertex 3: \((-8, -7)\) → Translated: \((-8+2, -7 - 1)=(-6, -8)\)
• Original vertex 4: \((-4, -8)\) → Translated: \((-4 + 2, -8-1)=(-2, -9)\)

To plot these points:

• For \((-3, -2)\): Move 3 units left of the origin on the x - axis and 2 units down on the y - axis.
• For \((-3, -5)\): Move 3 units left on the x - axis and 5 units down on the y - axis.
• For \((-6, -8)\): Move 6 units left on the x - axis and 8 units down on the y - axis.
• For \((-2, -9)\): Move 2 units left on the x - axis and 9 units down on the y - axis.

(Note: The key is to apply the translation rule \((x,y)\to(x + 2,y - 1)\) to each original vertex. The actual plotting is done on the coordinate grid by marking these new points.)