Question

Guadrilateral whose vertices are A(-2-2),B(5-2),C(4-3) and D(-3,-3)what kind of a guadrilatetal is ABCD?

Answer 1

The quadrilateral ABCD is a parallelogram

Explanation:

The vertices of the quadrilateral ABCD are;

A(-2 -2), B(5, -2), C(4, -3)and D(-3, -3)

The slope of segment
`\overline {AB}` = (-2 - (-2))/(5 - (-2)) = 0

The length of segment
`\overline {AB}` = 5 - (-2) = 7 (points having the same y-coordinates)

The slope of segment
`\overline {AD}` = (-3 - (-2))/(-3 - (-2)) = 1

The length of segment
`\overline {AD}` = √((-3 - (-2))² + (-3 - (-2))²) = √2

The slope of segment
`\overline {DC}` = (-3 - (-3))/(-3 - 4) = 0

The length of segment
`\overline {DC}` = 4 - (-3) = 7 (points having the same y-coordinates)

The slope of segment
`\overline {BC}` = (-3 - (-2))/(4 - 5) = 1

The length of segment
`\overline {AD}` = √((4 - 5)² + (-3 - (-2))²) = √2

Therefore;

The opposite sites of the quadrilateral ABCD are equal;
`\overline {AB}` =
`\overline {DC}`,
`\overline {AD}` =
`\overline {BC}`

Given that the slope of a line gives the inclination of the line on a graph, we have;

The opposite sites of the quadrilateral are parallel;
`\overline {AB}` ║
`\overline {DC}`,
`\overline {AD}` ║
`\overline {BC}`

Therefore the quadrilateral ABCD is a parallelogram because the opposite sides of the quadrilateral ABCD are parallel.