8-108. Draw a coordinate graph and plot the following points: A(-1,-1), B(2,2), C(4,-2). Connect the points in onder and then connect point C to point A. Which point could you move to make this an obtuse triangle? (Remember that an obtuse triangle is a triangle with one angle greater than 90°.) What would be the new point?

1. Draw the Coordinate Graph:

   • Draw the x-axis (horizontal) and y-axis (vertical) on a graph paper or using graphing software.
   • Label the axes with appropriate scales.

2. Plot the Points:

   • Point A(-1, -1): Move 1 unit to the left on the x-axis and 1 unit down on the y-axis.
   • Point B(2, 2): Move 2 units to the right on the x-axis and 2 units up on the y-axis.
   • Point C(4, -2): Move 4 units to the right on the x-axis and 2 units down on the y-axis.

3. Connect the Points in Order:

   • Draw a line segment from A to B.
   • Draw a line segment from B to C.
   • Draw a line segment from C to A.

4. Identify the Triangle:

   • You now have triangle ABC with vertices at A(-1, -1), B(2, 2), and C(4, -2).

5. Determine the Angle Types:

   • To determine if the triangle is obtuse, you need to check the angles. An obtuse triangle has one angle greater than 90°.

6. Move a Point to Make the Triangle Obtuse:

   • To make the triangle obtuse, you can move one of the points such that one of the angles becomes greater than 90°.
   • Let's consider moving point B. If you move point B to a new location, you need to ensure that one of the angles becomes obtuse.

7. Find the New Point:

   • One possible new location for point B could be (0, 3). This would change the shape of the triangle and potentially create an obtuse angle.

8. Verify the New Triangle:

   • Plot the new point B(0, 3) on the graph.
   • Connect the points A(-1, -1), B(0, 3), and C(4, -2).
   • Check the angles to ensure that one of them is greater than 90°.

By moving point B to (0, 3), you can create an obtuse triangle with one angle greater than 90°.