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In the XY-plane, lines l and k intersect at the point
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13 Jan 2024, 01:00
13 Jan 2024, 01:00
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In the XY-plane, lines \(\ell\) and \(k\) intersect at the point (\(\frac{16}{5}\), \(- \frac{12}{5}\) ) . The product of the slopes of lines \(\ell\) and \(k\) is −1. If line k passes through the origin, what is the slope of line l?
Give your answer as a fraction.
Give your answer as a fraction.
Show: ::
\(\frac{4}{3}\)
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GRE Geometry Formulas
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In the XY-plane, lines l and k intersect at the point
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18 Jan 2024, 22:26
18 Jan 2024, 22:26
1
The equation for lines is \(y = mx + b\)
Given that line k passes through the origin, b = 0.
Use the point \((\frac{16}{5}, -\frac{12}{5})\) to solve for m:
\(-\frac{12}{5} = m(\frac{16}{5})\)
\(-\frac{12}{16} = m\)
\(m = -\frac{3}{4}\)
Let n = the slope of line l. Since the product of the slopes of the lines is -1, m*n = -1.
\(-\frac{3}{4}*n = -1\)
\(m = \frac{4}{3}\)
Given that line k passes through the origin, b = 0.
Use the point \((\frac{16}{5}, -\frac{12}{5})\) to solve for m:
\(-\frac{12}{5} = m(\frac{16}{5})\)
\(-\frac{12}{16} = m\)
\(m = -\frac{3}{4}\)
Let n = the slope of line l. Since the product of the slopes of the lines is -1, m*n = -1.
\(-\frac{3}{4}*n = -1\)
\(m = \frac{4}{3}\)
gmatclubot
In the XY-plane, lines l and k intersect at the point [#permalink]
18 Jan 2024, 22:26
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