Question

Determine the endpoints of the midsegment connecting side YX and side YZ.Question options:A) (4, 3) and (8, 0)B) (4, 3) and (5, –1)C) (1, 2) and (7, 4)D) (9, –4) and (7, 4)

Answer 1

Answer:

B ; (4,3) and (5,-1)

Explanation:

Here, we want to get the coordinates of the endpoints of the midsegments

Let us firstly give a representation of what we are to calculate:

Now, from the above, what we are to calculate are the coordiantes of the points A and B

If we notice, the point A is the midpoint of the line XY

the point B is the midpoint of YZ

By simply finding the midpoint coordiantes of these lines, we will able to get what we are looking for

We start as follows:

$(x,y)\text{ = (}\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})$

The above will give us the coordiantes of the midpoints

Let us get the coordinates of the individual vertex points

X is (7,4)

Y is (1,2)

Z is (9,-4)

So, for point A that lies between X and Y, we have its coordiante as:

$(x,y)\text{ = (}\frac{7+1_{}}{2},\frac{4+2}{2})\text{ = (4,3)}$

Lastly for point B that lies between Y and Z , we have:

$(x,y)\text{ = (}\frac{1+9}{2},\frac{2-4}{2})\text{ = (5,-1)}$