Hints for solving the problems - Apply 3.1

Plotting Points – problems 1-15

Every problem has an order pair in the form of: (x, y)

For example problem number 7. (-1, -5)(For these assignments it is helpful if you use graph paper). Start at the origin (0, 0). Go one unit left (because of the -1) and from that point go 5 units down (because of the -5). You should be at the point: (-1, -5).

Problems 19-24

Problem No. 19 – Start at the origin(0, 0) move left under the M and that is 4 units to the left (-4). Then move up three units (+3) and you land on the M. So the ordered pair is: (-4, 3). You do not have to put the + sign in front of a positive number.

Problems 25-26

Remember any ordered pair like (5, 6) (both positive) is in the first quadrant.

Remember any ordered pair like (-5, 6) (first negative and second positive) is in the second quadrant.

Remember any ordered pair like (-5, -6) (first negative and second negative) is in the third quadrant.

Remember any ordered pair like (5, -6) (first positive and second negative) is in the fourth quadrant.

Problem No. 27.   (1, -3)  first (+),   second (-)   4^th quadrant

Rise and Run

The rise is the distance from one point to the other moving upward (+) or downward(-).

The run is the distance from one point to the other moving left (-) or right(+).

Problems 29-56

Problem 31 - Find the rise and run in moving from the point (11, 5) to the point (2, 9).

Plot the point (11, 5) and the point (2, 9). Start at the point (11, 5) and move left (horizontal) until you are above 2 and then move up to 9. So you have moved 9 units to the left and 4 units up.

The rise is 4 and the run is -9.

The distance formula (Using the Pythagorean Theorem) (a² + b² = c²)

Problem no. 59 - Use a = 15 and b = 36. Substitute the numbers into the formula.           (15)² + (36)² = c² 225 + 1296 = c²       1521 = c²

       c = 39 (square root of both sided yields 39).

Remember c must be the largest number, because it is the hypotenuse, which is opposite the right angle of a right triangle and the largest side.

Problems 61-66

Use the general formula for the equation of a circle:   (x - h)² + (y – k)² = r²

(h, k) is the center of the circle and the square root of r² is the radius (r).

Problem 61  -     (2, -3)   r = 4

When going from the ordered pair to the formula and vice versa change the sign of h and k.

         (x - 2) ² + (y + 3)² = 16   Ans.

Problems 67-72

Use the distance formula:   

Problem No. 69  -  (7, 2) 7 is x₁, 2 is y₁     (-8, 3) -8 is x₂, 3 is y₂.

Substitute into the formula:  

                   ans.

Problems 73-78

Problem No. 75 - Look at the graph. Start at the point on the left (-2, -5), move right until you are under the other point (a distance of 6 units) (a = 6).

The go up from that point until you reach the other ordered pair. (a distance of 8) (b = 8). Pythagorean Theorem :     6² + 8² = c²     36 + 64 = c²

              100 = c²     c = 10

Problems 79-84

Problem No. 79 - The equation of the circle:    (x + 5)² + (y + 2)² = 3²

The center is (h, k) The opposite of 5 is -5 and the opposite of 2 is -2.

So the center is (-5, -2). The radius is the square root of 3².

So the radius is 3.