Show that the line joining $(2, - 3)$ and $(- 5, 1)$ is parallel to the line joining $(7, - 1)$ and $(0, 3)$

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Solution

Slope of $(2, - 3)$ and $(- 5, 1)$ is $\frac{1 + 3}{- 5 - 2} = \frac{4}{- 7} = m_{1}$

Slope of $(7, - 1)$ and $(0, 3)$ is

$\frac{3 + 1}{0 - 7} = \frac{4}{7} = m_{2}$

Since $m_{1} = m_{2}$ , we can say that the lines are parallel.

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Show that the line joining (2,−3) and (−5,1) is parallel to the line joining (7,−1) and (0,3)

Slope of (2,−3) and (−5,1) is 1+3−5−2=4−7=m1Slope of (7,−1) and (0,3) is3+10−7=47=m2Since m1=m2, we can say that the lines are parallel.

Show that the line joining $(2, - 3)$ and $(- 5, 1)$ is parallel to the line joining $(7, - 1)$ and $(0, 3)$

Slope of $(2, - 3)$ and $(- 5, 1)$ is $\frac{1 + 3}{- 5 - 2} = \frac{4}{- 7} = m_{1}$

Slope of $(7, - 1)$ and $(0, 3)$ is

$\frac{3 + 1}{0 - 7} = \frac{4}{7} = m_{2}$

Since $m_{1} = m_{2}$ , we can say that the lines are parallel.