Let's take these one at a time.
Given two points and
the midpoint is then given by:
Now, can you post your attempts using this formula?
1. Use the midpoint formula. Find the midpoint between the following points.
- A(1,4) and B(5,6).
- A(4, 6) and B(-2, -2)
- A(3, -4) and B(5, 4)
- A(-3,2) and B(6,0)
2. Use the distance formula. Find the distance between the points in Problem 1, above.
3. Calculate the slopes of the lines determined by the points in Problem 1.
4. Find the equations of the lines determined by the points in Problem 1. Write the equations in slope-intercept form.
5. Plot each point of the following points, and connect them to form the triangle ABC. Find the area of the triangle using two techniques; Heron's Formula, and the three-point coordinate formula (see Math Open Reference, 2009). Show your work in detail. Prove that both methods yield the same results.
- A(-2,5); B(1, 3); C(-1,0)
- A(-5,3); B(6, 0); C(5,5)
- A(4,-3); B(0,-3); C(4,2)
- A(4,-3); B(4, 1); C(2,1)