Find the values of x and y if (−3,−2) is the midpoint of the line connecting the points (−2,1) and (x,y).
To find the midpoint of a line, we use the formula:
Midpoint = ((x1 + x2)/2, (y1 + y2)/2)
Given that the midpoint is (-3, -2) and the points are (-2, 1) and (x, y), we can set up the following equations:
x1 + x2 = 2*(-3)
y1 + y2 = 2*(-2)
Substitute the known values:
-2 + x = -6
1 + y = -4
Solving for x and y:
x = -6 + 2 = -8
y = -4 - 1 = -5
Therefore, the values of x and y are -8 and -5 respectively.