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two vertices of rectangle abcd are located at a(-7,-6) and b(3,-6). if the midpoint of line ad is located 2 units down from a, what is the length of AD? What are the coordinates of the vertices C and D?

Sagot :

Semsee45idn

Answer:

AD = 4 units

C(3, -10)

D(-7, -10)

Step-by-step explanation:

The midpoint of a line segment is the point that is exactly halfway between its two endpoints. Given that the midpoint of line segment AD is located 2 units down from A, it tells us that D must be directly below A along the same vertical line, making AD a vertical line segment. Therefore, D is 4 units below A, and the length of AD is:

[tex]\sf \overline{\sf AD}=4\;units[/tex]

Since A and D are on the same vertical line, the x-coordinate of D is the same as the x-coordinate of A, and the y-coordinate of D can be found by subtracting 4 from the y-coordinate of A. Therefore, the coordinates of vertex D are:

[tex]\sf D=(-7,-6-4)\\\\D=(-7,-10)[/tex]

Since ABCD is a rectangle and points A(-7, -6) and B(3, -6) are on the same horizontal line (having the same y-coordinate), and points A(-7, -6) and D(-7, -10) are on the same vertical line (having the same x-coordinate), the x-coordinate of C will be the same as B, and the y-coordinate of C will be the same as D. Therefore, the coordinates of vertex C are:

[tex]\sf C=(3,-10)[/tex]

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