midpoint of L. 1/3XY = 3.
What is the midpiont of XY?
1/3XY = 3,
Multiply both sides by 3:
xy = 9,
Mid-point = 9/2 = 4.5
If triangle ÄXYZ is equilateral and the length of one side is 7.5, what is the perimeter of ÄXYZ and what is the measure of each angle?
To find the midpoint of a line segment, you need to know the coordinates of its endpoints. In this case, we know that the line segment XY is divided into two parts, with a ratio of 1/3 to 2/3. Let's start by assigning coordinates to the endpoints of XY.
Let's assume the coordinates of point X are (x1, y1) and the coordinates of point Y are (x2, y2). Now, according to the given ratio, the distance between point X and the midpoint M is one-third of the distance between X and Y. Hence, we can find the coordinates of the midpoint as follows:
x-coordinate of midpoint M = (1/3 * x2) + (2/3 * x1)
y-coordinate of midpoint M = (1/3 * y2) + (2/3 * y1)
Substituting the given ratio and coordinates, we get:
x-coordinate of midpoint M = (1/3 * 3) + (2/3 * x1)
= 1 + (2/3 * x1)
= (x1 + 3) / 3
Similarly,
y-coordinate of midpoint M = (1/3 * 0) + (2/3 * y1)
= (2/3 * y1)
= (2/3 * y1)
Therefore, the midpoint of XY is ( (x1 + 3) / 3, (2/3 * y1) ).