Answer:
Midpoint Formula
Step-by-step explanation:
I just took the test sorry :(
The midpoint of a segment on the coordinate plane is given by half the
sum of the coordinates of the boundaries.
Reasons:
The given parameters are;
The theorem to be proven: The segment joining the midpoint of two triangle is parallel to the third side and half its length.
The coordinates of the vertex point A = (6, 8)
Coordinates of the vertex point B = (2, 2)
The coordinates of the vertex point C = (8, 4)
The point D, is the midpoint of AB and the point E is the midpoint of BC
The midpoint formula is presented as follows; [tex]\displaystyle \mathbf{\left(\frac{x_1 + x_2}{2}, \, \frac{y_1 + y_2}{2} \right)}[/tex]
Therefore, we have;
[tex]\displaystyle Midpoint \ of \ AB, \ which \ is \ point \ D = \left(\frac{6 + 2}{2} , \, \frac{8 + 2}{2} \right) = \mathbf{(4, \, 5)}[/tex]
[tex]\displaystyle Midpoint \ of \ BC, \ which \ is \ point \ E = \mathbf{\left(\frac{8 + 2}{2} , \, \frac{4 + 2}{2} \right)} = (5, \, 3)[/tex]
The distance (length) formula is; d = [tex]\sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}[/tex]
The length of segment DE = √((5 - 4)² + (3 - 5)²) = √5
The length of segment AC = √((8 - 6)² + (4 - 8)²) = 2·√5
The two column proof is presented as follows;
[tex]\begin{tabular}{lcl}Statement &&Reason\\1.The coord of point D are (4, 5) \& the coord of point E are (5, 3)&&1.\\The length of DE is \sqrt{5} \ \mathrm{and \ the \ length \ of \ segment \ AC \ is \ 2\cdot \sqrt{5}} &&Distance formula\\Segment DE is half the length of segment AC&&Substitution property \\Slope of DE is -2 and slope of AC is -2 &&Slope formula\\Segment DE is parallel to segment AC&&Slope of \parallel lines \ are = \end{array}[/tex]
The option that completes the proof, the reason for statement 1. is a. By the midpoint formula
Statement [tex]{}[/tex] Reason
The coordinate of point D are (4, 5) and [tex]{}[/tex] By the midpoint formula
the coordinate of point E are (5, 3)
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