Let's break down the given information and solve for the coordinates of Point D.
1. Point A has coordinates \((-9, 4)\).
2. Point D and Point A have the same second coordinate, meaning Point D's y-coordinate is also 4.
We are told that line segment \(AD\) is 3 cm in length. However, to determine the coordinates of Point D on the coordinate plane, we need to convert this physical measurement to units on the coordinate plane. Since no scale is provided for conversion, we assume the length refers to units on the coordinate plane.
3. The length of 3 units on the coordinate plane specifically refers to the distance between the x-coordinates because the y-coordinates are the same (both \(y = 4\)).
If \(AD\) is horizontal (since the y-coordinates are the same), the x-coordinates must differ by 3 units.
Given Point A at \((-9, 4)\), there are two potential points for Point D, depending on whether \(AD\) extends to the right or left:
- Extending to the right:
\( D = (-9 + 3, 4) = (-6, 4) \)
- Extending to the left:
\( D = (-9 - 3, 4) = (-12, 4) \)
Conclusively, the coordinates of Point D could be either \((-6, 4)\) or \((-12, 4)\).
Use the image to answer the question.
An illustration shows a coordinate plane with the x axis extending from negative 11 to 2 and the y axis extending from negative 3 to 10 in increments of 1. Points upper A,upper B, and upper C are plotted in quadrant 2. Upper A is plotted at left parenthesis negative 9 comma 4 right parenthesis. Upper B is plotted at left parenthesis negative 11 comma 1 right parenthesis. Upper C is plotted at left parenthesis negative 2 comma 1 right parenthesis.
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?
1 answer