Q(-8,3), R(6,3), S(3,-3), T(-11,-3)
Which of the following is the strongest classification that identifies this quadrilateral?
Since QR || ST and QT || RS we have a parallelogram.
Since QR ≠ RS, it is not a rhombus.
Since QR is not perpendicular to RS, it is not a rectangle.
So, parallelogram is a strong as we get.
To determine the classification of the quadrilateral using the given points, we need to analyze its properties. The classification of a quadrilateral is typically based on its sides and angles. Let's start by finding the lengths of the sides and measuring the angles.
Step 1: Find the lengths of the sides.
To find the lengths of the sides, we can use the distance formula, which is given by:
Distance = √((x2 - x1)^2 + (y2 - y1)^2)
Using this formula, we can calculate the lengths of the sides:
- Side QR:
Distance = √((6 - (-8))^2 + (3 - 3)^2) = √((14)^2 + (0)^2) = √(196) = 14
- Side RS:
Distance = √((3 - 6)^2 + (-3 - 3)^2) = √((-3)^2 + (-6)^2) = √(9 + 36) = √(45) = 3√5
- Side ST:
Distance = √((-11 - 3)^2 + (-3 - 3)^2) = √((-14)^2 + (-6)^2) = √(196 + 36) = √(232) = 2√58
- Side TQ:
Distance = √((-11 - (-8))^2 + (-3 - 3)^2) = √((-11 + 8)^2 + (-6)^2) = √((-3)^2 + (-6)^2) = √(9 + 36) = √(45) = 3√5
Step 2: Measure the angles.
To classify the quadrilateral, we also need to measure the angles between the sides. To do this, we can use the slope formula:
Slope (m) = (y2 - y1) / (x2 - x1)
By calculating the slopes of each side, we can find the measures of the angles between the sides.
- Angle QRS:
Slope of QR = (3 - 3) / (6 - (-8)) = 0 / 14 = 0
Slope of RS = (-3 - 3) / (3 - 6) = (-6) / (-3) = 2
Since the slopes are different, the angle QRS is not a right angle (90 degrees).
- Angle RST:
Slope of RS = (-3 - 3) / (3 - 6) = (-6) / (-3) = 2
Slope of ST= (-3 - (-3)) / (3 - (-11)) = 0 / 14 = 0
Since the slopes are different, the angle RST is not a right angle (90 degrees).
- Angle STQ:
Slope of ST = (-3 - (-3)) / (3 - (-11)) = 0 / 14 = 0
Slope of TQ= (3 - 3) / (-8 - (-11)) = 0 / 3 = 0
Since the slopes are the same, the angle STQ is a right angle (90 degrees).
- Angle TQR:
Slope of TQ = (3 - 3) / (-8 - (-11)) = 0 / 3 = 0
Slope of QR= (3 - 3) / (6 - (-8)) = 0 / 14 = 0
Since the slopes are the same, the angle TQR is a right angle (90 degrees).
Step 3: Classify the quadrilateral.
Based on the side lengths and angle measurements, we can classify the quadrilateral:
- Since all four sides of the quadrilateral have different lengths, it is not an equilateral, isosceles, or parallelogram.
- Since two adjacent sides are perpendicular (STQ and TQR) and all angles are 90 degrees, the quadrilateral can be classified as a rectangle.
Therefore, the strongest classification for this quadrilateral is a rectangle.