Question

The coordinates of the vertices of quadrilateral JKLM are J(-4, 1), K(2, 3), L(5, -3), and M(0, -5). Find the slopes of the line segments JK, LK, ML, and MJ. Is quadrilateral JKLM a parallelogram?

1) Yes, because there are two pairs of equal slopes, and thus two pairs of parallel sides.
2) No, because there are no pairs of parallel sides.
3) Cannot be determined.
4) Not enough information given.

Answer 1

The slopes of the line segments JK, LK, ML, and MJ are 1/3, -2, 2/5, and -3/2 respectively. Quadrilateral JKLM is not a parallelogram because the slopes of opposite sides are not equal.

Step-by-step explanation:

To find the slopes of the line segments, we can use the formula: slope = (change in y)/(change in x).

1. For segment JK, the coordinates are J(-4, 1) and K(2, 3). The slope is (3-1)/(2-(-4)) = 2/6 = 1/3.
2. For segment LK, the coordinates are L(5, -3) and K(2, 3). The slope is (3-(-3))/(2-5) = 6/-3 = -2.
3. For segment ML, the coordinates are M(0, -5) and L(5, -3). The slope is (-3-(-5))/(5-0) = 2/5.
4. For segment MJ, the coordinates are M(0, -5) and J(-4, 1). The slope is (1-(-5))/(-4-0) = 6/-4 = -3/2.

To determine if quadrilateral JKLM is a parallelogram, we compare the slopes of opposite sides. The slopes of segments JK and ML are 1/3 and 2/5 respectively, which are not equal. Therefore, quadrilateral JKLM is not a parallelogram.