Frank Math 2 Distance And Midpoint

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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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).

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].

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.