what is the x and y co-ordinate of the midpoint of the line segment

Question

 Consider the two points (3 ,-3 ) and (10 ,6 ). The distance between them is ?

The x co-ordinate of the midpoint of the line segment that joins them is ?
The y co-ordinate of the midpoint of the line segment that joins them is ?

Answer 1

Dalia,

 

Introduce a third point at (x=10, y=-3) using the x value of the second point and the y value of the first point. Then connect all the points with line segments. You've now formed a right triangle with a side parallel to the x-axis and a side parallel to the y-axis.  Then

 

Delta x = 10 -3 = 7 = length of side parallel to x-axis

Delta y = 6 - (-3) = 9 length of side parallel to y-axis

It's hypotenuse c just connects the original two points, so calculate it using the formula c² = (Delta x)² + (Delta y)².

So c2 = 49 + 81 = 130 and c = 11.40 approximately = distance between the original points

 

From geometry, the midpoint of the hypotenuse occurs at the midpoints of the Delt x and Delta y segments.  Hence,

The x-coordinate of the midpoint = 3 + 7/2   = 6.5

The y-coordinate of the midpoint = -3 + 9/2  = 1.5

So the midpoint (x,y) = (6.5, 1.5)