- Whiteboard
- Flag
-
In the diagram above, coordinates are given for three of the vertices of quadrilateral ABCD. Does quadrilateral ABCD have an area greater than 30?
(1) point B has an x-coordinate of 4
(2) quadrilateral ABCD is a parallelogram
Title
Cartesian Parallelogram
Your Result
Correct
Difficulty
Hard
Your Pace
0:02
Others' Pace
2:02
Video Explanation
Text Explanation
In this problem, the lower triangle ACD has a base of AC = 8, and a height, from the origin down to D, of 4. Therefore, the area of ACD = bh = ()(8)(4) = 16. We would need to know something about the upper triangle ABC to know the answer to the prompt question. We know the base of triangle ABC, AC = 8, but we don't know anything about the height.
Statement #1: if we know the x-coordinate of point B, that doesn't help us. We still know the base AC = 8, but we don't know the height, only the vertical line along which point B will lie. Any height could be possible. This statement, alone and by itself, is insufficient.
Statement #2: the diagonal of any parallelogram (i.e. the line connecting two opposite vertices) divides it into two congruent triangles. Well, if ABCD is a parallelogram, then line AC is a diagonal, which means triangles ADC and ABD must be congruent and have equal area. This would allow us to calculate the total area and answer the prompt question. This statement, alone and by itself, is sufficient.
Answer = B
Related Lessons
Watch the lessons below for more detailed explanations of the concepts tested in this question. And don't worry, you'll be able to return to this answer from the lesson page.
