Explore Westonci.ca, the premier Q&A site that helps you find precise answers to your questions, no matter the topic. Our platform offers a seamless experience for finding reliable answers from a network of knowledgeable professionals. Get quick and reliable solutions to your questions from a community of experienced experts on our platform.
Sagot :
To find the coordinates of the fourth vertex of a rectangle when three of its vertices are given, we can follow these steps:
1. Identify Given Points:
The vertices given are:
- [tex]\( A = (-2, 3) \)[/tex]
- [tex]\( B = (4, 3) \)[/tex]
- [tex]\( C = (4, -3) \)[/tex]
2. Understand the Properties of a Rectangle:
In a rectangle, opposite sides are parallel and equal in length, and all interior angles are right angles (90 degrees).
3. Check Alignment of Given Points:
- Points [tex]\( A \)[/tex] and [tex]\( B \)[/tex] have the same [tex]\( y \)[/tex]-coordinate, which means the line segment [tex]\( AB \)[/tex] is horizontal.
- Points [tex]\( B \)[/tex] and [tex]\( C \)[/tex] have the same [tex]\( x \)[/tex]-coordinate, meaning the line segment [tex]\( BC \)[/tex] is vertical.
4. Determine Missing Coordinates:
- We need to find point [tex]\( D \)[/tex] such that [tex]\( D \)[/tex] forms a rectangle with the given points [tex]\( A, B, \)[/tex] and [tex]\( C \)[/tex].
- For [tex]\( D \)[/tex] to align with the properties of a rectangle, it must share the [tex]\( y \)[/tex]-coordinate of point [tex]\( C \)[/tex] and the [tex]\( x \)[/tex]-coordinate of point [tex]\( A \)[/tex].
5. Combine Identified Coordinates:
- The [tex]\( x \)[/tex]-coordinate of point [tex]\( D \)[/tex] should match the [tex]\( x \)[/tex]-coordinate of point [tex]\( A \)[/tex]: [tex]\( -2 \)[/tex].
- The [tex]\( y \)[/tex]-coordinate of point [tex]\( D \)[/tex] should match the [tex]\( y \)[/tex]-coordinate of point [tex]\( C \)[/tex]: [tex]\( -3 \)[/tex].
Therefore, the coordinates of the fourth vertex [tex]\( D \)[/tex] are:
[tex]\[ (-2, -3) \][/tex]
1. Identify Given Points:
The vertices given are:
- [tex]\( A = (-2, 3) \)[/tex]
- [tex]\( B = (4, 3) \)[/tex]
- [tex]\( C = (4, -3) \)[/tex]
2. Understand the Properties of a Rectangle:
In a rectangle, opposite sides are parallel and equal in length, and all interior angles are right angles (90 degrees).
3. Check Alignment of Given Points:
- Points [tex]\( A \)[/tex] and [tex]\( B \)[/tex] have the same [tex]\( y \)[/tex]-coordinate, which means the line segment [tex]\( AB \)[/tex] is horizontal.
- Points [tex]\( B \)[/tex] and [tex]\( C \)[/tex] have the same [tex]\( x \)[/tex]-coordinate, meaning the line segment [tex]\( BC \)[/tex] is vertical.
4. Determine Missing Coordinates:
- We need to find point [tex]\( D \)[/tex] such that [tex]\( D \)[/tex] forms a rectangle with the given points [tex]\( A, B, \)[/tex] and [tex]\( C \)[/tex].
- For [tex]\( D \)[/tex] to align with the properties of a rectangle, it must share the [tex]\( y \)[/tex]-coordinate of point [tex]\( C \)[/tex] and the [tex]\( x \)[/tex]-coordinate of point [tex]\( A \)[/tex].
5. Combine Identified Coordinates:
- The [tex]\( x \)[/tex]-coordinate of point [tex]\( D \)[/tex] should match the [tex]\( x \)[/tex]-coordinate of point [tex]\( A \)[/tex]: [tex]\( -2 \)[/tex].
- The [tex]\( y \)[/tex]-coordinate of point [tex]\( D \)[/tex] should match the [tex]\( y \)[/tex]-coordinate of point [tex]\( C \)[/tex]: [tex]\( -3 \)[/tex].
Therefore, the coordinates of the fourth vertex [tex]\( D \)[/tex] are:
[tex]\[ (-2, -3) \][/tex]
Thank you for visiting. Our goal is to provide the most accurate answers for all your informational needs. Come back soon. Thank you for your visit. We're committed to providing you with the best information available. Return anytime for more. We're dedicated to helping you find the answers you need at Westonci.ca. Don't hesitate to return for more.