Distance and Midpoint Homework

Name: Math 2

Date:

Distance and Midpoint Homework

1. Write an expression for the distance between the points named.

a. (a, b) and (c, d) b. (e,-f) and (-g, -h)

2. There are twelve points, each with integer coordinates that are 10 units from the origin. List the points.

3. List twelve points, each with integer coordinates, that are 5 units from (-8, 1)

4. Show that a triangle with vertices A(-3,4), M(3,1), and Y(0,-2) is isosceles.

5. Quadrilateral TAUL has vertices T(4,6), A(6,-4), U(-4,-2), and L(-2, 4). Show that the diagonals are congruent.

6. Show that the triangle with vertices A(3,-1), B(5,1), and C(-1,1) is a scalene triangle.

7. Find the area of the rectangle with vertices B(8,0), T(2,-9), R(-1,-7), and C(5,2).

8. It is known that is isosceles. G is point (-2,-3); H is point (-2,7); the x-coordinate of M is 4. Find all five possible values for the y-coordinate of M.

9. Discover and prove two things about the triangle with vertices K(-3,4), M(3,1), and J(-6,-2).

10. The point (a, b) is equidistant from (-2,5), (8,5), and (6,7). Find the values of a and b.

11. Find the length of the median of the trapezoid with vertices C(-4,-3), D(-1,4), E(4,4) and F(7,-3). The median is the segment that connects the midpoints of the legs of a trapezoid. The legs of a trapezoid are the non-parallel sides.

12. The vertices of a parallelogram are K(6,0), O(0,0), S(2,4), E(8,4).

a. Show that OK=SE and OS=KE. What conclusion can you draw about the sides of a parallelogram?

b. Find and compare the midpoint of segments OE and KS.

c. What conclusion can you draw about the diagonals of a parallelogram?

13. The vertices of right triangle OAT are O(0,0), A(0,8), and T(-6,0).

a. If M is the midpoint of AT, what are the coordinates of M?

b. Find and compare the lengths of MA, MT, and MO.

c. What conclusion can you draw about the midpoint of the hypotenuse of a right triangle?