Frank Math 2 Distance And Midpoint

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| By Courtney Frank

Courtney Frank

Community Contributor

Quizzes Created: 44 | Total Attempts: 15,791

Questions: 5 | Attempts: 159 | Updated: Mar 20, 2023

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Questions and Answers

1.

Calculate the midpoint between the points (4, -2) and (-8, 6).
- A.
  
  (6, 4)
- B.
  
  (-6, -4)
- C.
  
  (2, 2)
- D.
  
  (-2, 2)
Correct Answer
D. (-2, 2)

Explanation
The midpoint between two points can be calculated by finding the average of their x-coordinates and the average of their y-coordinates. In this case, the average of the x-coordinates is (4 + (-8))/2 = -2, and the average of the y-coordinates is (-2 + 6)/2 = 2. Therefore, the midpoint is (-2, 2).

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2.

Find the distance between the points (3, -2) and (6, 4).
- A.
- B.
- C.
- D.
Correct Answer
D.

Explanation
The distance between two points in a coordinate plane can be found using the distance formula, which states that the distance between two points (x1, y1) and (x2, y2) is equal to the square root of [(x2 - x1)^2 + (y2 - y1)^2]. Applying this formula to the given points (3, -2) and (6, 4), we have: distance = sqrt[(6 - 3)^2 + (4 - (-2))^2] = sqrt[3^2 + 6^2] = sqrt[9 + 36] = sqrt[45]. Therefore, the distance between the two points is sqrt[45].

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3.

If point S (4, 2) is the midpoint between points R and T, what is point R if the coordinates of T are (9, 17)?
- A.
  
  (-13, -1)
- B.
  
  (-1, -13)
- C.
  
  (4, 2)
- D.
  
  (8, 4)
Correct Answer
B. (-1, -13)

Explanation
The midpoint formula states that the coordinates of the midpoint between two points (x1, y1) and (x2, y2) is ((x1 + x2)/2, (y1 + y2)/2). In this case, we are given that point S (4, 2) is the midpoint between points R and T. We are also given that the coordinates of T are (9, 17). To find the coordinates of R, we can use the midpoint formula. Plugging in the values, we get ((x1 + 9)/2, (y1 + 17)/2) = (4, 2). Solving for x1 and y1, we get x1 = -1 and y1 = -13. Therefore, the coordinates of R are (-1, -13).

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4.

What is the distance between the 2 points shown?
- A.
  
  5
- B.
- C.
  
  7
- D.
Correct Answer
D.
5.

If the distance between the points (2, 9) and (5, y) is , what are the possible values of y?
- A.
  
  4 and 14
- B.
  
  -4 and -14
- C.
  
  -4 and 14
- D.
  
  4 and -14
Correct Answer
A. 4 and 14

Explanation
The distance between two points can be found using the distance formula, which is the square root of the sum of the squares of the differences in the x-coordinates and the y-coordinates. In this case, the x-coordinate of the first point is 2 and the x-coordinate of the second point is 5. Since the x-coordinate difference is 3, the y-coordinate difference must also be 3 in order for the distance to be a whole number. Therefore, the possible values of y are 9 + 3 = 12 and 9 - 3 = 6. So, the correct answer is 4 and 14.

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