Quadrilateral PQRS is not a rectangle because it has only one right angle.
Answer:
Option A is correct.
As, Quadrilateral PQRS is not a rectangle because it has only one right angle.
Explanation:
Given:
The coordinate of vertices of quadrilateral PQRS are P(−4,2), Q(3, 4), R(5,0) and S(−3,−2).
Slope for two points [tex](x_{1},y_{1})[/tex] and [tex](x_{2},y_{2})[/tex] is given by:
[tex]\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex].
The slope of PQ is [tex]\frac{4-2}{3-(-4)} =\frac{2}{7}[/tex]
The slope of QR is [tex]\frac{0-4}{5-3} =\frac{-4}{2} = -2[/tex]
The slope of RS is [tex]\frac{-2-0}{-3-5} =\frac{-2}{-8} =\frac{1}{4}[/tex]
The slope of SP is [tex]\frac{2-(-2)}{-4-(-3)} =\frac{4}{-1} =-4[/tex]
The slopes of perpendicular lines are opposite reciprocals.
∴ only one pair of sides has slopes that are negative reciprocals;
this means the figure has only 1 right angle, so it is not a rectangle.
Therefore, quadrilateral PQRS is not a rectangle because it has only one right angle.
