a line segment is drawn from A(14,10) to B(6,4). Find the distance from A to the midpoint of the segment.
To find the distance from point A to the midpoint of segment AB, we first need to find the coordinates of the midpoint of the segment.
The x-coordinate of the midpoint is the average of the x-coordinates of points A and B:
Midpoint x-coordinate = (14 + 6) / 2 = 20 / 2 = 10
The y-coordinate of the midpoint is the average of the y-coordinates of points A and B:
Midpoint y-coordinate = (10 + 4) / 2 = 14 / 2 = 7
So, the coordinates of the midpoint of segment AB is M(10,7).
Now, we can use the distance formula to find the distance from A(14,10) to M(10,7):
Distance = √[(x2 - x1)² + (y2 - y1)²]
Distance = √[(10 - 14)² + (7 - 10)²]
Distance = √[(-4)² + (-3)²]
Distance = √[16 + 9]
Distance = √25
Distance = 5
Therefore, the distance from point A to the midpoint of segment AB is 5 units.