Question

PLEASE HELP!!!

You are graphing quadrilateral ABCD in the coordinate plane. The length of segment AB is the same as the length of segment DC, and both segments are horizontal. The following are three vertices of quadrilateral: A (1, 1), C (4.5, 4), and D (-1.5,4). All you know about point B is that is in the first quadrant.

What are the coordinates of point B?

Answer 1

To find the coordinates of point B in the first quadrant, calculate the distance between points C and D, and add it to point A's x-coordinate. The coordinates of point B are (7, 1).

Step-by-step explanation:

To find the coordinates of point B in the quadrilateral ABCD, we take into account that segments AB and DC are equal in length and both are horizontal. Since we have the coordinates of points A (1, 1), C (4.5, 4), and D (-1.5,4), we can deduce the length of segment DC (or AB) by calculating the distance between points C and D, which are both on the same horizontal level (y-coordinate of 4).

The distance between C and D is the absolute difference in their x-coordinates: |4.5 - (-1.5)| = 6.0 units. Since AB is horizontal and of the same length, we add this distance to the x-coordinate of A to find the x-coordinate of B. The y-coordinate of B would be the same as that of A, as segment AB is horizontal.

So the x-coordinate of B is 1 + 6.0 = 7.0. Therefore, the coordinates of point B are (7, 1).