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SAT Math : Perpendicular Lines

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Example Question #1 : Perpendicular Lines

Which of the following lines is perpendicular to $y=3x-4$

Possible Answers:

$y=\frac{1}{3}x-4$

$y=\frac{1}{3}x+4$

$y=-3x-4$

$y=-\frac{1}{3}x-4$

Correct answer:

$y=-\frac{1}{3}x-4$

Explanation:

The line which is perpendicular has a slope which is the negative inverse of the slope of the original line.

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Example Question #51 : Perpendicular Lines

Trans

Lines P and Q are parallel. Find the value of .

Possible Answers:

$x=-5- \sqrt{ 205}$

$x=\pm \sqrt{ 205}$

$x=5 + \sqrt{ 205}$

$x=-5+ \sqrt{ 205}$

$x= \sqrt{ 205}$

Correct answer:

$x=-5+ \sqrt{ 205}$

Explanation:

Since these are complementary angles, we can set up the following equation.

x^2+4+10x-4=180

x^2+10x=180

x^2+10x-180=0

Now we will use the quadratic formula to solve for .

$x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$

$x=\frac{-10\pm \sqrt{10^2-4(1)(-180)}}{2(1)}$

$x=\frac{-10\pm \sqrt{100+720}}{2}$

$x=\frac{-10\pm \sqrt{820}}{2}$

$x=\frac{-10\pm \sqrt{4\cdot 205}}{2}$

$x=\frac{-10\pm 2\sqrt{ 205}}{2}$

$x=-5\pm \sqrt{ 205}$

Note, however, that the measure of an angle cannot be negative, so $x=-5- \sqrt{ 205}$ is not a viable answer. The correct answer, then, is $x=-5+ \sqrt{ 205}$

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SAT Math : Perpendicular Lines

Study concepts, example questions & explanations for SAT Math

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Example Question #1 : Perpendicular Lines

Example Question #51 : Perpendicular Lines

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