Finding Distance in the Coordinate Plane /Instruction/ assignment

Which points can be used in the diagram as the third vertex to create a right triangle with hypotenuse XY? Select all that apply. (-4, -2) (-2, 1) (-2, -2) (2, 4) (3, 4)

(-2, -2) (3, 4)

Use the drop downs to answer the following questions of finding the distance from (-6, 2) to the origin. Use (0, 0) as (x1, y1). d = StartRoot (x 2 minus x 1) squared + (y 2 minus y 1) squared EndRoot What is the difference of the x-coordinates, (x2-x1)? What is the difference of the y-coordinates, (y2-y1)? What is the distance from (-6, 2) to the origin?

-6 2 6.32

Enter a number that correctly completes the following statement. The point (12, 5) is units from the origin.

13

Use the drop downs to answer the following questions about the distance between the points (−5, 1) and (2, −1). What is the distance of the horizontal leg? What is the distance of the vertical leg? Use the Pythagorean theorem. What is the distance between the two points?

7 2 53

Use the Pythagorean theorem to find the distance on the coordinate plane. a2 + b2 = c2 What is the distance between the two points? StartRoot 20 EndRoot StartRoot 40 EndRoot StartRoot 45 EndRoot StartRoot 58 EndRoot

StartRoot 58 EndRoot

George calculated the distance between (2, 4) and (6, 3) using the distance formula. His work is shown below. 1. d = StartRoot (6 minus 2) squared + (3 minus 4) squared EndRoot. 2. d = StartRoot (4) squared + (negative 1) squared EndRoot. 3. d = StartRoot 16 + 1 EndRoot. 4. d = StartRoot 17 EndRoot Analyze George's work. Is he correct? If not, what was his mistake? Yes, he is correct. No, he substituted values in the wrong places. No, he didn't use the proper order of operations. No, he evaluated the powers incorrectly.

Yes, he is correct

Find the distance between the points (a, 0) and (0, b). StartRoot (a minus b) squared EndRoot StartRoot a squared + b squared EndRoot StartRoot (a + b) squared EndRoot StartRoot a squared minus b squared EndRoot

b

The new location for a park needs to be exactly 5 miles from the school. When plotted on the coordinate plane, the school is located at (3, 3). Use the Pythagorean theorem to determine two possible locations on the coordinate plane for the park. (-3, -3) (-1, 0) (0, 0) (6, -1) (6, 6)

b and d

Which triangle would be most helpful in finding the distance between the points (-4, 3) and (1, -2) on the coordinate plane?

c

What is the distance between the points (-4, 2) and (3, -5)? d = StartRoot (x 2 minus x 1) squared + (y 2 minus y 1) squared EndRoot StartRoot 10 EndRoot StartRoot 28 EndRoot StartRoot 98 EndRoot StartRoot 117 EndRoot

c 98

Which equation would find the distance between the two points show on the coordinate plane? d = StartRoot (x 2 + x 1) squared + (y 2 + y 1) squared EndRoot d = StartRoot (x 2 minus x 1) squared minus (y 2 minus y 1) squared EndRoot d = StartRoot (x 2 minus x 1) squared + (y 2 minus y 1) squared EndRoot

d = StartRoot (x 2 minus x 1) squared + (y 2 minus y 1) squared EndRoot

Use the distance formula to find the distance between (-3, 5) and (3,1). d = StartRoot (x 2 minus x 1) squared + (y 2 minus y 1) squared EndRoot d = 4 d = StartRoot 20 EndRoot d = StartRoot 42 EndRoot d = StartRoot 52 EndRoot

d = StartRoot 52 EndRoot

Use the distance formula to find the distance between (−8, 2.5) and (0, −4.5). d = StartRoot (x 2 minus x 1) squared + (y 2 minus y 1) squared EndRoot 1. Substitute coordinates: d = StartRoot (negative 8 minus 0) squared + (2.5 minus (negative 4.5)) squared EndRoot 2. Simplify parentheses: d = StartRoot (negative 8) squared + (7) squared EndRoot 3. Evaluate powers: d = StartRoot 64 + 49 EndRoot 4. Simplify. What is the distance between (-8, 2.5) and (0, -4.5)? Round to the nearest hundredth. d ≈

d ≈ 10.63

Triangle XYZ is a right triangle. Use the drop downs to determine the length of the legs of the right triangle. What is the length of Side X Z? What is the length of Size Y Z?

xz 5 yz 6

What is distance between point X and point Y? √11 √22 √61 √72

√61