1. \(\sqrt{5}, \; \left( \frac{1}{2}, \, 1 \right)\)
2. \( 2 \sqrt{2}, \; (2, \, 4) \)
3. \(\sqrt{ 7 – 2 \sqrt{2}}, \; \left( 0, \, \frac{ 1 + \sqrt{2} }{2}\right) \)

5. \(B = (3, \, 9)\)
6. \(A = (-1, \, 18)\)

13. \( (2, \, 2)\) and \((-4, \, 2)\)
14. \((1, \, 13)\) and \((1, \, -11)\)
15. \(5x + 2y – 3 = 0\)
16. \(x^2 + y^2 = 9\)
17. \((1, \, -3), \, (3, \, 1), \, (-5, \, 7)\)
18. \( (-2, \, -5), \, (0, \, -9)\)
19. \(\left( \frac{9}{2}, \, 1 \right)\)

For exercises 1 through 3, calculate the distance between points \(\boldsymbol{P}\) and \(\boldsymbol{Q}\) and determine the midpoint of segment \(\boldsymbol{\overline{PQ}}\).

1. \[ P = (0, 0)\text{, } \, Q = (1, 2) \]
2. \[ P = (1, 3)\text{, } \, Q = (3, 5) \]
3. \[ P = (-1, 1)\text{, } \, Q = (1, \sqrt{2}) \]
4. Prove that the points \(A = (-2, 4)\), \(B = (-1, 3)\)   and   \(C = (2, -1)\) are collinear.
5. If \(A = (-3, -5)\), \(M = (0, 2)\) and \(M\) is the midpoint of the segment \(\overline{AB}\), find \(B\).
6. If \(B = (8, -12)\), \(M = (7/2, 3)\) and \(M\) is the midpoint of the segment \(\overline{AB}\), find \(A\).
7. Prove that \(A = (2, -3)\), \(B = (4, 2)\) and \(C = (-1, 4)\) are the vertices of an isosceles triangle.
8. Prove that \(A = (4, 1)\), \(B = (2, 2)\) and \(C = (-1, -4)\) are the vertices of a right triangle.
9. Prove that \(A = (1, 2)\), \(B = (4, 8)\), \(C = (5, 5)\) and \(D = (2, -1)\) are the vertices of a parallelogram.
10. Prove that \(A = (0, 2)\), \(B = (1, 1)\), \(C = (2, 3)\) and \(D = (-1, 0)\) are the vertices of a rhombus.
11. Prove that \(A = (1, 1)\), \(B = (11, 3)\), \(C = (10, 8)\) and \(D = (0, 6)\) are the vertices of a rectangle.
12. Prove that \(A = (-4, 1)\), \(B = (1, 3)\), \(C = (3, -2)\) and \(D = (-2, -4)\) are the vertices of a square.
13. Find the points \(P = (x, 2)\) whose distance to the point \((-1, -2)\) is 5 units.
14. Find the points \(P = (1, y)\) whose distance to the point \((-4, 1)\) is 13 units.
15. Find an equation in terms of the two variables, \(x\) and \(y\), satisfied by the coordinates of all points P = (x, y), equidistant from the points \(A = (6, 1)\) and \(B = (-4, -3)\).
16. Find an equation in terms of the two variables, \(x\) and \(y\), satisfied by the coordinates of all points \(P = (x, y)\) with a distance of 3 units from the origin.
17. The midpoints of the sides of a triangle are \(M = (2, -1)\), \(N = (-1, 4)\) and \(Q = (-2, 2)\). Find the vertices.
18. Two adjacent vertices of a parallelogram are \(A = (2, 3)\) and \(B = (4, -1)\). If the the point \(M = (1, -3)\) bisects the diagonals, find the other two vertices.
19. The vertices of a quadrilateral are \(A = (-2, 14)\), \(B = (3, -4)\), \(C = (6, -2)\) and \(D = (6, 6)\). Find the intersection point of the diagonals.