Final answer:
The coordinates of the other endpoint given the midpoint and one endpoint are (11, 6). To find the distance between two points, we use the distance formula which gives approximately 8 units for the distance between (5,8) and (-2,3).
Step-by-step explanation:
To find the coordinate of the other endpoint given the midpoint (5,5) and one endpoint (-1,4), we can use the midpoint formula. The midpoint formula states that the midpoint's coordinates are the averages of the endpoints' coordinates. Therefore, if (x1, y1) is the known endpoint and (xm, ym) is the midpoint, then:
- xm = (x1 + x2) / 2
- ym = (y1 + y2) / 2
Solving for x2 and y2:
- x2 = 2 * xm - x1
- y2 = 2 * ym - y1
In this case, (xm, ym) = (5,5) and (x1, y1) = (-1, 4). So:
- x2 = 2 * 5 - (-1) = 11
- y2 = 2 * 5 - 4 = 6
So the coordinates of the other endpoint are (11, 6), making option (d) the correct answer.
For finding the distance between (5,8) and (-2,3), we can use the distance formula:
- d = √[(x2 - x1)^2 + (y2 - y1)^2]
Plugging in the coordinates:
- d = √[(-2 - 5)^2 + (3 - 8)^2]
- d = √[(7)^2 + (-5)^2]
- d = √[49 + 25]
- d = √[74]
- d = 8.6023, which we round down to 8 for the nearest whole number.
Hence, the distance between the points is approximately 8 units, making option (d) the correct answer.