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كويز تفاعلي: Determine whether lines are parallel, perpendicular, or neither
Determine whether $\overleftrightarrow{AB}$ and $\overleftrightarrow{CD}$ are parallel, perpendicular, or neither. Graph each line to verify your answer. This worksheet involves calculating the slope of lines passing through given coordinate points and identifying their relationship. Parallel lines have equal slopes ($m_1 = m_2$), while perpendicular lines have slopes that are negative reciprocals ($m_1 \cdot m_2 = -1$).
يرجى الانتباه إلى أن المعلم قام بإعداد الأسئلة فقط، ولم يقم بإعداد الإجابات أو الشروحات المرفقة. وقد تم توليد الإجابات باستخدام تقنيات الذكاء الاصطناعي، لذلك قد تتضمن بعض الأخطاء أو عدم الدقة.
للحصول على الإجابات الصحيحة والمضمونة، يُرجى الرجوع إلى المعلم أو المصدر الدراسي المعتمد.
Question 1
Points: 1
Determine whether $\overleftrightarrow{AB}$ and $\overleftrightarrow{CD}$ are parallel, perpendicular, or neither for the points: A(1, 5), B(4, 4), C(9, -10), D(-6, -5)
Explanation
The slope of AB is $m = \frac{4 - 5}{4 - 1} = -\frac{1}{3}$. The slope of CD is $m = \frac{-5 - (-10)}{-6 - 9} = \frac{5}{-15} = -\frac{1}{3}$. Since the slopes are equal, the lines are parallel.
Question 2
Points: 1
Determine whether $\overleftrightarrow{AB}$ and $\overleftrightarrow{CD}$ are parallel, perpendicular, or neither for the points: A(-6, -9), B(8, 19), C(0, -4), D(2, 0)
Explanation
The slope of AB is $m = \frac{19 - (-9)}{8 - (-6)} = \frac{28}{14} = 2$. The slope of CD is $m = \frac{0 - (-4)}{2 - 0} = \frac{4}{2} = 2$. Since the slopes are equal, the lines are parallel.
Question 3
Points: 1
Determine whether $\overleftrightarrow{AB}$ and $\overleftrightarrow{CD}$ are parallel, perpendicular, or neither for the points: A(4, 2), B(-3, 1), C(6, 0), D(-10, 8)
Explanation
The slope of AB is $m = \frac{1 - 2}{-3 - 4} = \frac{1}{7}$. The slope of CD is $m = \frac{8 - 0}{-10 - 6} = -\frac{1}{2}$. The slopes are not equal and their product is not -1, so they are neither.
Question 4
Points: 1
Determine whether $\overleftrightarrow{AB}$ and $\overleftrightarrow{CD}$ are parallel, perpendicular, or neither for the points: A(8, -2), B(4, -1), C(3, 11), D(-2, -9)
Explanation
The slope of AB is $m = \frac{-1 - (-2)}{4 - 8} = -\frac{1}{4}$. The slope of CD is $m = \frac{-9 - 11}{-2 - 3} = 4$. Since the product of the slopes is -1, the lines are perpendicular.
Question 5
Points: 1
Determine whether $\overleftrightarrow{AB}$ and $\overleftrightarrow{CD}$ are parallel, perpendicular, or neither for the points: A(8, 4), B(4, 3), C(4, -9), D(2, -1)
Explanation
The slope of AB is $m = \frac{3 - 4}{4 - 8} = \frac{1}{4}$. The slope of CD is $m = \frac{-1 - (-9)}{2 - 4} = -4$. Since the product of the slopes is -1, the lines are perpendicular.
Question 6
Points: 1
Determine whether $\overleftrightarrow{AB}$ and $\overleftrightarrow{CD}$ are parallel, perpendicular, or neither for the points: A(4, -2), B(-2, -8), C(4, 6), D(8, 5)
Explanation
The slope of AB is $m = \frac{-8 - (-2)}{-2 - 4} = 1$. The slope of CD is $m = \frac{5 - 6}{8 - 4} = -\frac{1}{4}$. The slopes are not equal and their product is not -1, so they are neither.
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