Graph the image of the figure after a dilation with a scale factor of 3 centered at (2,-7)

Question

Graph the quadrilateral by connecting all its vertices.

(I'm not able to atach the image for some wierd reson so I will list the points of the orignal shape)

(-2,-7),(0,-4),(4,-5),(3,-3)

Answer 1

To perform a dilation with a scale factor of 3 centered at (2, -7), you'll follow these steps for each point:

1. Subtract the center of dilation from the original point to find the vector from the center to the original point.
2. Multiply this vector by the scale factor (3 in this case).
3. Add the center of dilation back to the scaled vector to find the coordinates of the dilated point.

Let's apply this process to each of the original points:

1. For the point (-2, -7):

   • Vector to center: \((-2 - 2, -7 - (-7)) = (-4, 0)\)
   • Scale the vector: \(3 \cdot (-4, 0) = (-12, 0)\)
   • Dilated point: \((2 + (-12), -7 + 0) = (-10, -7)\)

2. For the point (0, -4):

   • Vector to center: \((0 - 2, -4 - (-7)) = (-2, 3)\)
   • Scale the vector: \(3 \cdot (-2, 3) = (-6, 9)\)
   • Dilated point: \((2 + (-6), -7 + 9) = (-4, 2)\)

3. For the point (4, -5):

   • Vector to center: \((4 - 2, -5 - (-7)) = (2, 2)\)
   • Scale the vector: \(3 \cdot (2, 2) = (6, 6)\)
   • Dilated point: \((2 + 6, -7 + 6) = (8, -1)\)

4. For the point (3, -3):

   • Vector to center: \((3 - 2, -3 - (-7)) = (1, 4)\)
   • Scale the vector: \(3 \cdot (1, 4) = (3, 12)\)
   • Dilated point: \((2 + 3, -7 + 12) = (5, 5)\)

Now, after the dilation with a scale factor of 3 centered at (2, -7), the new points are:

• (-10, -7)
• (-4, 2)
• (8, -1)
• (5, 5)

You can graph these points and connect them to form the dilated quadrilateral:

1. Plot the points on a coordinate plane:

   • A point at (-10, -7)
   • A point at (-4, 2)
   • A point at (8, -1)
   • A point at (5, 5)

2. Connect these points in the order they were listed to form the quadrilateral.

This gives you the dilated figure!