اختبار اختيار من متعدد 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 ($m_1 \cdot m_2 = -1$).
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اختبار شهادة تدريبي مؤقت للصف والمادة والفصل نفسه.
اختر إجابة واحدة لكل سؤال. عند الاختيار ستظهر النتيجة فورًا: الأخضر صحيح، والأحمر خطأ، وسيظهر تفسير الإجابة مباشرة إن كان متوفرًا. وبعد آخر سؤال ستظهر الدرجة النهائية تلقائيًا.
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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