the three vertices of rectangle ABCD are A(2, 1) , B(6, 1) , C(6, 4).Find the coordinates of D. Please help me,thank you.
note that A and B are on the same horizontal line.
So, D must also be in line vertically with A and horizontally with C, at (2,4)
To find the coordinates of vertex D, we need to consider the properties of a rectangle.
In a rectangle, opposite sides are parallel and equal in length. Additionally, the diagonals of a rectangle are equal in length and bisect each other.
Given the coordinates of vertices A, B, and C, we can use this information to find the coordinates of vertex D.
1. Start by plotting the points A(2, 1), B(6, 1), and C(6, 4) on a coordinate plane.
2. Draw a line segment connecting points A and B. Similarly, draw a line segment connecting points B and C. These line segments represent the sides of the rectangle.
3. Determine the length and slope of line AB. Since points A and B have the same y-coordinate (1), the line AB is horizontal. The length of AB can be found by calculating the difference in x-coordinates: 6 - 2 = 4 units.
4. Find the equation of the line that passes through point C and is perpendicular to AB. Since AB is horizontal, the line through C will be vertical. This means that its equation will be of the form x = k, where k is a constant. Since point C has an x-coordinate of 6, the equation of the line would be x = 6.
5. Determine where the line x = 6 intersects the line segment AB. Since the equation of line AB is y = 1 (since both A and B have a y-coordinate of 1), we can substitute x = 6 into the equation y = 1 to find the intersection point. Thus, the point of intersection is D(6, 1).
Therefore, the coordinates of vertex D are (6, 1).