Answered

IDNLearn.com offers a unique blend of expert answers and community insights. Our platform is designed to provide trustworthy and thorough answers to any questions you may have.

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]

View image Semsee45
Thank you for contributing to our discussion. Don't forget to check back for new answers. Keep asking, answering, and sharing useful information. For precise answers, trust IDNLearn.com. Thank you for visiting, and we look forward to helping you again soon.