On a design plan for a landscaping project, a straight path runs from A(11, 29) to B(53, 9). A lamp is going to be placed halfway along the path. 1. Determine the coordinates of the lamp's location. 2. Determine the length of the path. 2. Determine the equation of each of the following lines. Leave the answer in the form Ax + By + C =0. a. The slope is -2, and the point (2, -3) is on the line. (3 marks) b. The lines passes through the points ( 3, 3) and (6, 9). (4 marks) Given the points A(-1, 6) and B(2, -3), find the following: (10 marks) a. The slope of AB b. Length of AB c. The coordinates of the midpoint of AB d. The equation of a line perpendicular to AB that passes through the point (4, 7). Leave your answer in the form Ax + By + C = 0. 4. The endpoints of the diameter of a circle are D(7, -2) and E(11, -8) a. Determine the coordinates of the centre of the circle (2 marks) b. Determine the length of the circle's radius (2 marks) 5. One endpoint of a line segment is (-7, 2). The midpoint of the line segment is (-1, -2). What are the coordinates of the other endpoint? (5 marks) Verify that the shape with vertices at P(-5, 2), Q(-1. 3). R(-2, -1), and S(-6, -2) is a rhombus. On a map, three towns are located at the coordinates A(5, 1), B(-2, 0), and C(4, 8). The township wants to build a new fire station that is the same distance from each town. Determine the coordinates where they should build the new fire station. (Hint] von cuse sell-developed snort TON notations- A builder wants to run a power line from the main line to his office site. On the site plan, the office located at (25, 18) while the main power line runs through the points (1, 5) and (29, 12). At what point should the builder connect to the main power line? What length of cable will he need