Exercise 119 Page 449

Let's add the lattice labels on axes of the given diagram.

We want to find the midpoints of all the given segments. Let's start with segment a.

Segment a

To find the midpoint, we should first find the coordinates of the endpoints of segment a.

We want to find the midpoint of line segment a. We can use the midpoint formula to do find it. M (x_1+x_2/2,y_1+y_2/2)Let's substitute the coordinates of the endpoint into the formula and simplify.

The midpoint of line segment a is the point M_a(4.5,3). Let's add it to the diagram.

Let's move on to segment b.

Segment b

Like for segment a, let's first find the coordinates of the endpoints of segment b.

To find the midpoint, let's again substitute the coordinates of the endpoints into the midpoint formula and simplify.

The midpoint of line segment b is the point M_b(-3, 1.5). Let's add it to the diagram.

Let's move on to segment c.

Segment c

Let's find the coordinates of the endpoints of segment c.

Now we can substitute the coordinates of the endpoints into the midpoint formula and simplify.

The midpoint of line segment c is the point M_c(1.5, -2). Let's add it to the diagram.

Our Findings

Now that we found all of the midpoints, let's list them with their coordinates M_a (4.5, 3) M_b (-3, 1.5) M_c (1.5, -2) We can also see the graph with of the midpoints and their coordinates.