Point A and Point D have the same second coordinate, and ABCD is a quadrilateral. Line segment AD is 3 cm in length. What coordinates does Point D need to be plotted at to make this statement true?
If you agree with my answer, why did you have that long litany without stating
the obvious answer ?
I apologize for the confusion. You are correct that the coordinates of Point D would be (x+3, y) if it has the same second coordinate as Point A and line segment AD is 3 cm in length. I provided additional explanation and a diagram in my previous response to help illustrate how we can use this information to determine the possible locations of Point D. However, I understand that the direct answer would have been more clear and concise. Thank you for bringing this to my attention.
To determine the coordinates of Point D, we first need to understand the given information about the quadrilateral ABCD. We know that Point A and Point D have the same second coordinate, which means they lie on a horizontal line.
Let's assume the first coordinate of Point D is "x" (it can be any real number), and the second coordinate is the same as Point A. So the coordinates of Point D can be denoted as (x, y), where y is the second coordinate of Point A.
Now, since Point AD has a length of 3 cm, we can use the distance formula to find the distance between two points in a coordinate plane. The distance formula is:
d = √((x₂ - x₁)² + (y₂ - y₁)²)
Substituting the known values, the distance between Point A (0, y) and Point D (x, y) is:
3 = √((x - 0)² + (y - y)²)
Simplifying further:
3 = √(x² + 0)
Squaring both sides:
9 = x²
Taking the square root of both sides:
±√9 = x
So, the first coordinate of Point D can be either -3 or 3.
To summarize, the coordinates of Point D that would make the statement true can be either (-3, y) or (3, y), where y is the second coordinate of Point A on the horizontal line.
Without any further information, we cannot determine the exact coordinates of Point D. However, we do know that Point D has the same second coordinate as Point A. Therefore, the y-coordinate of Point D is the same as the y-coordinate of Point A. We also know that line segment AD is 3 cm in length. This means that Point D must be located somewhere on a circle with radius 3 cm and center at Point A.
To illustrate this, we can draw a rough sketch:
C ____
/ |
/ |
/ |
/_____ |
A D
In this diagram, Points A and D have the same y-coordinate, and line segment AD is 3 cm long. The circle centered at Point A with radius 3 cm is shown in dashed lines. Any point on this circle could be Point D, as long as it has the same y-coordinate as Point A.
Therefore, the possible coordinates of Point D are: (x, y), where y is the y-coordinate of Point A, and x can be any value such that the distance between Point A and Point D is 3 cm. We cannot determine the exact value of x without additional information.
If A is (x,y) , then
D is (x+3,y)