Exercise 5 Page 398

Let's begin by recalling that the midpoint of a segment is the point that divides the segment into 2 congruent segments. To find the midpoint, we can use the Midpoint Formula. Let's recall it!

The Midpoint Formula
The coordinates of the midpoint of a segment are the averages of the x-coordinates and of the y-coordinates

Let A( x_1, y_1) and B( x_2, y_2) be the endpoints of a segment AB. Then the midpoint of this segment has the following coordinates. (x_1+ x_2/2,y_1+ y_2/2) Now we are given that the coordinates of the endpoints are A(1,2) and B(7,8). Let's use these to find the coordinates of the midpoint M.

M(x_1+x_2/2,y_1+y_2/2)

SubstitutePoints

Substitute ( 1,2) & ( 7,8)

M(1+ 7/2,2+ 8/2)

AddTerms

Add terms

M(8/2,10/2)

CalcQuot

Calculate quotient

M(4,5)

The midpoint M is located at point (4,5). Let's plot the given points in the coordinate plane to better visualize the solution.