Question

Point A and point D have the same second coordinate, and ABCD is a quadrilateral. Line segment AD is 3 cm on length. What coordinates does point D need to be plotted at to make this state my true?

Answer 1

To find the coordinates of point D, we need to consider the information given in the problem:

1. Point A and point D have the same second coordinate: This means that the y-coordinate of point A and point D are the same.

2. Line segment AD is 3 cm in length: This means that the distance between point A and point D is 3 cm.

Let's assume that the second coordinate of point A and point D is y.

Let the coordinates of point A be (x1, y) and the coordinates of point D be (x2, y).

Since line segment AD is 3 cm in length, we have:
(x2 - x1)^2 + (y - y)^2 = 3^2

(x2 - x1)^2 = 9

So, x2 - x1 = 3 or x2 - x1 = -3

Since point D can be either to the right or left of point A, we need to consider both cases. Let's calculate the coordinates in each case:

Case 1: x2 - x1 = 3
In this case, if point D is to the right of point A by 3 cm, the coordinates will be:
Point A: (x1, y)
Point D: (x1 + 3, y)

Case 2: x2 - x1 = -3
In this case, if point D is to the left of point A by 3 cm, the coordinates will be:
Point A: (x1, y)
Point D: (x1 - 3, y)

Therefore, the coordinates of point D can be either (x1 + 3, y) or (x1 - 3, y), depending on the direction of point D relative to point A.