Solve the following problems. Draw the figure for each item.

1. The vertices of a triangle are at (1, 7), (6, -1) and (0, 3). Find the coordinates of the midpoints of the sides.

2. The segment from (-1, 4) to (2, 2) is extended three times its own length. Find the terminal point.

3. The segment joining (2,-4), (2, 3) is divided into two segments, one of which is three fourths as long as the other. Find the point of division. Ans. (6, 0) and (5,-1)

4. The circle with its center at (4,-2) has one end of the diameter at (7, 2). Find the coordinates of the other end of this diameter.

5.A person 6 ft. tall is standing near a street light so that he is 4/10 of the distance form the pole to the tip of his shadows. How high above the ground is the light bulb?

Here are the diagrams for each problem:

1. **Midpoints of the Triangle**: This figure shows the triangle with vertices \((1, 7)\), \((6, -1)\), and \((0, 3)\), along with the midpoints of each side.

2. **Extension of Segment**: The segment from \((-1, 4)\) to \((2, 2)\) is extended three times its length, resulting in the terminal point at \((11, -4)\).

3. **Division of Segment**: The vertical segment from \((2, -4)\) to \((2, 3)\) is divided at the point \((2, 0)\), creating two segments in the ratio of 3:4.

4. **Diameter of the Circle**: The circle centered at \((4, -2)\) with one end of the diameter at \((7, 2)\) has its other end at \((1, -6)\).

5. **Streetlight and Shadow**: This simplified diagram shows the person and the streetlight, where the light is 15 feet above the ground.

Would you like more details on any of these problems or have any questions?

Here are 5 related questions:
1. How can you determine the area of a triangle given its vertices?
2. How do you find the equation of a line given two points?
3. What is the midpoint theorem, and how is it applied in geometry?
4. How can you find the equation of a circle given its center and radius?
5. What role do proportions play in similar triangles and real-life applications?

**Tip:** In geometry, visualizing problems by sketching diagrams can greatly aid in understanding and solving complex problems.

Explore geometry problems involving triangles, segments, and circles with detailed solutions. Includes finding midpoints, extending segments, dividing segments, and circle diameters. Suitable for high school level students.

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