Two points X and Y in the xy plane have coordinates (10,5) and (a,b), respectively. The midpoint of the line segment XY has coordinates (13,13). What is the value of a+b?
To find the midpoint of a line segment, you can use the midpoint formula:
Midpoint = (($x_1$ + $x_2$) / 2, ($y_1$ + $y_2$) / 2)
Given that the midpoint of the line segment XY is (13,13), you can equate the coordinates:
(13, 13) = (($10$ + a) / 2, ($5$ + b) / 2)
Now, let's solve for a and b.
From the x-coordinate of the midpoint, we have:
(($10$ + a) / 2) = 13
Multiply both sides by 2:
$10$ + a = 26
Now, subtract 10 from both sides:
a = 26 - 10 = 16
From the y-coordinate of the midpoint, we have:
(($5$ + b) / 2) = 13
Multiply both sides by 2:
$5$ + b = 26
Now, subtract 5 from both sides:
b = 26 - 5 = 21
Therefore, the value of a + b is:
a + b = 16 + 21 = 37
So, the value of a + b is 37.