Please show solutions for these below:

1. Determine the equation of a line that is parallel to 4 + 2 = 7 and passes through (- 1, - 4).

2. How long is the perpendicular line segment between the parallel lines 4 3 + 12 = 0 and 4 3 18 = 0?

3. Consider the circles below.

a) The points (11, 4) and (- 3, 2) are the endpoints of a diameter of a circle. Determine the coordinates of the center of the circle.

b) Another diameter of the same circle has endpoint (- 1, 8). Determine the coordinates of the other endpoint.

4. Points (, - 7) and (4, ) are on the circle with equation 2 + 2 = 50. Determine the possible values of and . Round to the nearest tenth if necessary.

5. Classify the triangle that is formed by the lines = 2 + 3, + 2 = 16, and 3 - - 4 = 0

a) by its angles [*only the 90 angle is important]

b) by its side lengths You may use DESMOS to visualize the triangle.

6. Consider the triangle with vertices U(4,3), V(0,5), and W(4, 3) to answer the following questions.

a) Verify that the median from the right angle to the hypotenuse is half as long as the hypotenuse.

b) Find an equation of the circle that passes through the vertices of UVW.