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Use the figure above of Quadrilateral ABCD to answer the following: Use the check list to determine which properties fit. You will need to find the distance and slope of AB, BC, CD, and AD. option 1 : Opposite sides (AB, CD and BC, AD) have equal slopes making the parallel to each other, making ABCD a parallelogram.option 2: There is only two sides that have equal slopes, making them parallel to each otheroption 3: The slope of adjacent sides (like AB and BC) have negative reciprocals for slopes, making them perpendicular, which makes four 90 degree anglesoption 4: The distance of the sides AB, BC, CD, and AD are all congruent option 5 : The distance of the sides AB and CD are congruent and BC and AD are congruent, making opposite sides congruent, but not all four sides

Use The Figure Above Of Quadrilateral ABCD To Answer The Following Use The Check List To Determine Which Properties Fit You Will Need To Find The Distance And S class=

Sagot :

Explanation:

First, let's draw the quadrilateral. So:

Then, the distance d and slope m between two points with coordinates (x1, y1) and (x2, y2) can be calculated as:

[tex]\begin{gathered} d=\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2} \\ m=\frac{y_2-y_1}{x_2-x_1} \end{gathered}[/tex]

So, the distance and slope of AB where A is (-5,3) and B is (0, 6) are:

[tex]\begin{gathered} d=\sqrt[]{(0-(-5))^2+(6-3)^2} \\ d=\sqrt[]{(0+5)^2+3^2} \\ d=\sqrt[]{34} \\ m=\frac{6-3}{0-(-5)}=\frac{3}{0+5_{}}=\frac{3}{5} \end{gathered}[/tex]

The distance and slope of BC where B is (0,6) and C is (5, 3) are:

[tex]\begin{gathered} d=\sqrt[]{(5-0)^2+(3-6)^2}=\sqrt[]{34} \\ m=\frac{3-6}{5-0}=-\frac{3}{5} \end{gathered}[/tex]

The distance and slope of CD where C is (5,3) and D is (0, 0) is:

[tex]\begin{gathered} d=\sqrt[]{(0-5)^2+(0-3)^2}=\sqrt[]{34} \\ m=\frac{0-3}{0-5}=\frac{-3}{-5}=\frac{3}{5} \end{gathered}[/tex]

The distance and slope of AD where A is (-5,3) and D is (0, 0) are:

[tex]\begin{gathered} d=\sqrt[]{(0-(-5))^2+(0-3)^2} \\ d=\sqrt[]{(0+5)^2+(3)^2}=\sqrt[]{34} \\ m=\frac{0-3}{0-(-5)}=-\frac{3}{5} \end{gathered}[/tex]

Therefore, the correct answers are:

Option 1 : Opposite sides (AB, CD, and BC, AD) have equal slopes making them parallel to each other, making ABCD a parallelogram.

Option 4: The distance of the sides AB, BC, CD, and AD are all congruent

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