MATH SOLVE

5 months ago

Q:
# The coordinates of the vertices of quadrilateral JKLM are J(−4, 1) , K(2, 3) , L(5, −3) , and M(0, −5) . Drag and drop the choices into each box to correctly complete the sentences.

Accepted Solution

A:

Given that the coordinates of the vertices of quadrilateral JKLM are J(−4, 1) , K(2, 3) , L(5, −3) , and M(0, −5) .

The slope of the line joining two points [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] is given by:

[tex]slope= \frac{y_2-y_1}{x_2-x_1} [/tex]

Part A.

Given that the coordinates of the J is (−4, 1) and of K is (2, 3)

The slope of line JK is given by:

[tex]slope= \frac{3-1}{2-(-4)} \\ \\ = \frac{2}{2+4} = \frac{2}{6} = \frac{1}{3} [/tex]

Part B:

Given that the coordinates of the L is (5, -3) and of K is (2, 3)

The slope of line LK is given by:

[tex]slope= \frac{3-(-3)}{2-5} \\ \\ = \frac{3+3}{-3} = \frac{6}{-3} = -2 [/tex]

Part C:

Given that the coordinates of the M is (0, -5) and of L is (5, -3)

The slope of line ML is given by:

[tex]slope= \frac{-3-(-5)}{5-0} \\ \\ = \frac{-3+5}{5} = \frac{2}{5}[/tex]

Part D:

Given that the coordinates of M is (0, -5) and of J is (−4, 1)

The slope of line MJ is given by:

[tex]slope= \frac{1-(-5)}{-4-0} \\ \\ = \frac{1+5}{-4} = \frac{6}{-4} = -\frac{3}{2} [/tex]

Thus, quadrilateral JKLM is not a parallelogram because the opposite slopes are not equal.

The slope of the line joining two points [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] is given by:

[tex]slope= \frac{y_2-y_1}{x_2-x_1} [/tex]

Part A.

Given that the coordinates of the J is (−4, 1) and of K is (2, 3)

The slope of line JK is given by:

[tex]slope= \frac{3-1}{2-(-4)} \\ \\ = \frac{2}{2+4} = \frac{2}{6} = \frac{1}{3} [/tex]

Part B:

Given that the coordinates of the L is (5, -3) and of K is (2, 3)

The slope of line LK is given by:

[tex]slope= \frac{3-(-3)}{2-5} \\ \\ = \frac{3+3}{-3} = \frac{6}{-3} = -2 [/tex]

Part C:

Given that the coordinates of the M is (0, -5) and of L is (5, -3)

The slope of line ML is given by:

[tex]slope= \frac{-3-(-5)}{5-0} \\ \\ = \frac{-3+5}{5} = \frac{2}{5}[/tex]

Part D:

Given that the coordinates of M is (0, -5) and of J is (−4, 1)

The slope of line MJ is given by:

[tex]slope= \frac{1-(-5)}{-4-0} \\ \\ = \frac{1+5}{-4} = \frac{6}{-4} = -\frac{3}{2} [/tex]

Thus, quadrilateral JKLM is not a parallelogram because the opposite slopes are not equal.