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Math Chapter 7 : Topic 5
Parallel and Perpendicular Slopes
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Two lines are parallel if their gradients are:
Reasoning: Parallel lines have the same slope$⟹ m_{1}=m_{2}$
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Two lines are perpendicular if:
Reasoning: Perpendicular lines satisfy $m_{1} . m_{2}=- 1$
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If slope of a line is $3$, slope of a parallel line is:
Reasoning: Parallel lines have equal slopes$⟹ m_{1}=m_{2}$
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If slope of a line is $2$, slope of perpendicular line is:
Reasoning: Negative reciprocal $⟹ 1/2$$m_{1} . m_{2}=- 1 ⟹ m_{2}=-$ $\frac{1}{m_{1}}$
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Which pair represents perpendicular lines?
Reasoning: Product $=- 1$ ; $m_{1} . m_{2}=- 1$
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Which pair represents parallel lines?
Reasoning: Equal slopes$⟹$parallel$⟹ m_{1}=m_{2}$
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If one line is horizontal, a perpendicular line is:
Reasoning: Horizontal $⟂$ vertical.
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Slope of line perpendicular to vertical line is:
Reasoning: Vertical $⟂$ horizontal$⟹$slope $=0$
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If slope of line is $-5$, slope of perpendicular line is:
Reasoning: Negative reciprocal of $- 5$ is $1/5$.$m_{1} . m_{2}=- 1 ⟹$ $m_{2}=-$ $\frac{1}{m_{1}}$
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Parallel lines never:
Reasoning: Parallel lines do not meet.
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If two lines have slopes $4$ and $-1/4$, they are:
Reasoning: Product $=- 1 ⟹$ $m_{1} . m_{2}=- 1 ⟹$ $m_{2}=-$ $\frac{1}{m_{1}}$
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Which slopes cannot be perpendicular?
Reasoning: Equal slopes$⟹$ parallel, not perpendicular.
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If slope of one line is $0$, slope of perpendicular line is:
Reasoning: Horizontal $⟂$ vertical$m_{1} . m_{2}=- 1 ⟹ m_{2}=-$ $\frac{1}{m_{1}}=-\frac{1}{0}=\infty$
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If slopes are equal but intercepts differ, lines are:
Reasoning: Same slope, different intercept$⟹$parallel$⟹ m_{1}=m_{2}$
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If slopes are equal and intercepts equal, lines are:
Reasoning: Completely identical lines.
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Which condition ensures perpendicularity?
Reasoning: Standard perpendicular condition$⟹ m_{1} . m_{2}=- 1$
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Slope of perpendicular to line $y=3x+2$ is:
Reasoning: Negative reciprocal of $3 ⟹ m_{1} . m_{2}=- 1 ⟹$ $m_{2}=-$ $\frac{1}{m_{1}}$
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Slope of parallel to $y=- 2x+5$ is:
Reasoning: Same slope$⟹ m_{1}=m_{2}$
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Which pair gives perpendicular lines?
Reasoning: Product $=- 1 ⟹ m_{1} . m_{2}=- 1$
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If slope of one line is $\frac{3}{4}$, perpendicular slope is:
Reasoning: Negative reciprocal$⟹ m_{1} . m_{2}=- 1 ⟹ m_{2}=-$ $\frac{1}{m_{1}}$
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If slopes are negative reciprocals, lines:
Reasoning: Definition of perpendicular lines.$m_{1} . m_{2}=- 1 ⟹ m_{2}=-$ $\frac{1}{m_{1}}$
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Parallel lines have same:
Reasoning: Gradient defines direction.
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If slopes are $0$ and $5$, lines are:
Reasoning: Product $\ne - 1$ and slopes not equal.
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Which slope pair gives vertical and horizontal lines?
Reasoning: Vertical (undefined), horizontal $(0)$.
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If two lines intersect at right angle, their slopes:
Reasoning: Perpendicular condition$⟹ m_{1} . m_{2}=- 1$
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