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

$Slope of line joining (2, -3) and (-5, 1) m_{1} = \frac{y_{2} - y_{1}}{x_{2} - x_{1}} = \frac{1 - (- 3)}{- 5 - 2} = \frac{4}{- 7} Slope of line joining (7, -1) and (0, 3) m_{2} = \frac{y_{2} - y_{1}}{x_{2} - x_{1}} = \frac{3 - (- 1)}{0 - 7} = \frac{4}{- 7} S i n c e m_{1} = m_{2}, the two lines are parralel$

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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 line joining (2, -3) and (-5, 1)m1=y2−y1x2−x1=1−(−3)−5−2=4−7Slope of line joining (7, -1) and (0, 3)m2=y2−y1x2−x1=3−(−1)0−7=4−7Since m1=m2, the two lines are parralel