19. M(8, 7) is the midpoint of . The coordinates of S are (9, 5). What are the coordinates of R? (8.5, 6) (7, 9) (16, 14) (10, 3)
Let the coordinates of R be (x, y). Since M is the midpoint of RS, we can use the midpoint formula to find the coordinates of R:
x = (8 + 9) / 2 = 8.5
y = (7 + 5) / 2 = 6
Therefore, the coordinates of R are (8.5, 6), so the correct answer is (8.5, 6).
To find the coordinates of R, we need to use the midpoint formula. The midpoint formula states that the coordinates of the midpoint M between two points (x1, y1) and (x2, y2) can be found by using the formula:
M = ((x1 + x2) / 2, (y1 + y2) / 2)
Given that M is the midpoint between S(9, 5) and R, which is (8, 7), we can set up the following equation:
(9 + x) / 2 = 8
(5 + y) / 2 = 7
Simplifying the equations:
9 + x = 16
5 + y = 14
Solving for x and y:
x = 16 - 9 = 7
y = 14 - 5 = 9
Therefore, the coordinates of R are (7, 9).
To find the coordinates of point R, we can use the midpoint formula. The midpoint formula states that the midpoint of a line segment with endpoints (x1, y1) and (x2, y2) is given by the coordinates:
((x1 + x2) / 2, (y1 + y2) / 2)
In this case, M(8, 7) is the midpoint of RS and S is given as (9, 5).
Let's substitute the values into the formula:
((x1 + 9) / 2, (y1 + 5) / 2) = (8, 7)
So we have:
(x1 + 9) / 2 = 8
Solving this equation for x1 gives us:
x1 + 9 = 16
x1 = 16 - 9
x1 = 7
Next, we have:
(y1 + 5) / 2 = 7
Solving this equation for y1 gives us:
y1 + 5 = 14
y1 = 14 - 5
y1 = 9
Therefore, the coordinates of point R are (7, 9).
So the correct option is (7, 9).