1.
Calculate the midpoint between the points (4, -2) and (-8, 6).
Correct Answer
D. (-2, 2)
Explanation
The midpoint between two points is calculated by finding the average of their x-coordinates and the average of their y-coordinates. In this case, the x-coordinate of the midpoint is (4 + (-8))/2 = -2, and the y-coordinate is (-2 + 6)/2 = 2. Therefore, the midpoint is (-2, 2).
2.
Find the distance between the points (3, -2) and (6, 4).
Correct Answer
D.
Explanation
To find the distance between two points, we can use the distance formula, which is derived from the Pythagorean theorem. The formula is: √((x2 - x1)^2 + (y2 - y1)^2). In this case, the points are (3, -2) and (6, 4). Plugging the values into the formula, we get: √((6 - 3)^2 + (4 - (-2))^2) = √(3^2 + 6^2) = √(9 + 36) = √45. Therefore, the distance between the two points is √45.
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)?
Correct Answer
B. (-1, -13)
Explanation
If point S is the midpoint between points R and T, it means that the coordinates of S are the average of the coordinates of R and T. In this case, the coordinates of T are given as (9, 17) and the coordinates of S are given as (4, 2). To find the coordinates of R, we can subtract the coordinates of S from twice the coordinates of T. Therefore, R = 2T - S = 2(9, 17) - (4, 2) = (18, 34) - (4, 2) = (14, 32). The correct answer is (-1, -13), which matches the coordinates of R.
4.
What is the distance between the 2 points shown?
Correct Answer
D.
5.
If the distance between the points (2, 9) and (5, y) is , what are the possible values of y?
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 squared differences in the x-coordinates and the y-coordinates. In this case, the x-coordinates are 2 and 5, and the y-coordinate of one point is 9. To find the possible values of y, we can substitute the given x and y values into the distance formula and solve for y. By substituting 2, 5, 9, and the distance into the formula, we can find that the possible values of y are 4 and 14.