Question

Suppose line segment XY has one endpoint at X(0, 0). If (3, 4) is the midpoint of XY, what are the coordinates of point Y?

a) (-6, -8)
b) (6, 8)
c) (3, 4)
d) (0, 0)

Answer 1

To find the coordinates of point Y in a line segment with a given midpoint, we can use the midpoint formula. In this case, the coordinates of point Y are (6, 8).

Step-by-step explanation:

To find the coordinates of point Y, we can use the midpoint formula. The midpoint formula states that the coordinates of the midpoint M(x,y) between two points (x1,y1) and (x2,y2) is given by:

x = (x1 + x2)/2 and y = (y1 + y2)/2

In this case, we are given that the midpoint M is (3, 4) and one endpoint X is (0, 0). We need to find the coordinates of point Y.

Using the midpoint formula, we can substitute the values:

x = (0 + x2)/2 = x2/2

y = (0 + y2)/2 = y2/2

Since (3, 4) is the midpoint, we can equate the expressions:

x2/2 = 3 => x2 = 6

y2/2 = 4 => y2 = 8

Therefore, the coordinates of point Y are (6, 8), which is option b) (6, 8).