Question

The diagonals of a parallelogram meet at the point (0, 1). One vertex of the parallelogram is located at (1, 3), and a second vertex is located at (2, 0). Find the locations of the remaining vertices and determine the most specific classification of this parallelogram. A. The locations of the remaining vertices are at (-2, 1) and (-1, -2). The most specific classification of this parallelogram is a square. B. The locations of the remaining vertices are at (-2, 1) and (-1, 2). The most specific classification of this parallelogram is a rhombus. C. The locations of the remaining vertices are at (-2, 2) and (-1, -1). The most specific classification of this parallelogram is a square. D. The locations of the remaining vertices are at (-2, 2) and (-1, 1). The most specific classification of this parallelogram is a rectangle.

          The diagonals of a parallelogram meet at the point (0, 1). One vertex of the parallelogram is located at (1, 3), and a second vertex is located at (2, 0). Find the locations of the remaining vertices and determine the most specific classification of this parallelogram. 

A. The locations of the remaining vertices are at (-2, 1) and (-1, -2). The most specific classification of this parallelogram is a square.
B. The locations of the remaining vertices are at (-2, 1) and (-1, 2). The most specific classification of this parallelogram is a rhombus.
C. The locations of the remaining vertices are at (-2, 2) and (-1, -1). The most specific classification of this parallelogram is a square.
D. The locations of the remaining vertices are at (-2, 2) and (-1, 1). The most specific classification of this parallelogram is a rectangle.

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Added by Joseph S.

Geometry A Common Core Curriculum

Ron Larson, Laurie Boswell 1st Edition

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Solved by Expert Allison Knapp

11/17/2021

Step 1

The slope of this line is (0-3)/(2-1) = -3. Using the point-slope form of a line, we have y - 3 = -3(x - 1). Simplifying, we get y = -3x + 6. Show more…

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The diagonals of a parallelogram meet at the point (0, 1). One vertex of the parallelogram is located at (1, 3), and a second vertex is located at (2, 0). Find the locations of the remaining vertices and determine the most specific classification of this parallelogram. A. The locations of the remaining vertices are at (-2, 1) and (-1, -2). The most specific classification of this parallelogram is a square. B. The locations of the remaining vertices are at (-2, 1) and (-1, 2). The most specific classification of this parallelogram is a rhombus. C. The locations of the remaining vertices are at (-2, 2) and (-1, -1). The most specific classification of this parallelogram is a square. D. The locations of the remaining vertices are at (-2, 2) and (-1, 1). The most specific classification of this parallelogram is a rectangle.

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Transcript

00:01 So in this problem, they give us the point where the diagonals meet in a parallelogram, which is right here at 0 .1.

00:09 And then also the locations of two of the vertices, 1 3 and 2 .0.

00:15 And they want us to determine which one of those options best fits this description.

00:21 So since this is the point where the diagonals are meeting, it's going to be the midpoint of both of these segments here.

00:29 So what i'm going to do is use the midpoint formula, x1 plus x2 over 2, comma, y1 plus y2 over 2.

00:42 And i'm first going to start with this vertex here, 13.

00:46 So that's going to be my x1y1.

00:53 And this is the midpoint 01.

00:57 So i'm going to set the x part of this formula equal to 0.

01:03 So i would do 1 plus x2 over 2 equals 0, since i'm trying to find that other end point, and multiply both sides by 2, which would still leave me of 0, and subtract the 1.

01:21 Then i'm going to do the same thing with the y part of the formula, so i'm going to plug this in for y1 and set it equal to 1.

01:29 So that would be 3 plus y2 over 2 equals 1.

01:36 Apply both sides by 2.

01:38 So 3 plus y2 equals 2 and subtract the 3.

01:45 So y2 equals negative 1.

01:46 So the first coordinate is negative 1, negative 1...

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