Question

Determine what the type of quadrilateral has vertices A(-3, 3).

B(3, 1), C(4, -3) and D(-2, -1) by finding the lengths and
slopes of the four sides.

Answer 1

To determine the type of quadrilateral with vertices A(-3, 3), B(3, 1), C(4, -3) and D(-2, -1), we calculate the lengths and slopes of the sides. The lengths of AB, BC, CD, and DA are 2√10, √17, 2√10, and 2√10 respectively. The slopes of AB, BC, CD, and DA are -1/3, -4, 1/3, and 1/3 respectively.

Step-by-step explanation:

To determine the type of quadrilateral with vertices A(-3, 3), B(3, 1), C(4, -3) and D(-2, -1), we need to find the lengths and slopes of the four sides.

First, we calculate the length of AB using the distance formula: AB = √[(x2 - x1)^2 + (y2 - y1)^2] = √[(3 - (-3))^2 + (1 - 3)^2] = √[36 + 4] = √40 = 2√10.

Next, we calculate the length of BC and CD in the same way: BC = √[(4 - 3)^2 + (-3 - 1)^2] = √[1 + 16] = √17, and CD = √[(-2 - 4)^2 + (-1 - (-3))^2] = √[36 + 4] = √40 = 2√10.

Finally, we calculate the length of AD: AD = √[(3 - (-3))^2 + (1 - (-1))^2] = √[36 + 4] = √40 = 2√10.

Now, let's find the slopes of the sides. The slope between A and B is given by: mAB = (y2 - y1) / (x2 - x1) = (1 - 3) / (3 - (-3)) = -2/6 = -1/3. Similarly, we find the slopes of BC, CD, and DA: mBC = (-3 - 1) / (4 - 3) = -4/1 = -4, mCD = (-1 - (-3)) / (-2 - 4) = 2/6 = 1/3, mDA = (1 - (-1)) / (3 - (-3)) = 2/6 = 1/3.

Based on the lengths and slopes of the sides, we can conclude that the quadrilateral ABCD is a parallelogram.