Show that the line joining (2, – 3) and (– 5, 1) is parallel to th

1.	Show that the line joining (2, – 3) and (– 5, 1) is parallel to the line joining (7, – 1) and (0, 3).
Answer» To Prove: The given line is parallel to another line. Proof: Let Assume the coordinate A(2, – 3) and B(– 5, 1), C(7, – 1) and D(0,3). The concept used: Slopes of the parallel lines are equal. The formula used: The slope of the line, m = \(\frac{y_2-y_1}{x_2-x_1}\) Now, The slope of AB = \(\frac{1-(-3)}{-5-2}\) The Slope of AB = \(\frac{4}{-7}\) Now, The slope of CD = \(\frac{3-(-1)}{0-7}\) The Slope of AB = \(\frac{4}{-7}\) So, The slope of AB = The slope of CD Hence, The given Lines are parallel to each other.

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

Answer»

To Prove: The given line is parallel to another line.

Proof: Let Assume the coordinate A(2, – 3) and B(– 5, 1), C(7, – 1) and D(0,3).

The concept used: Slopes of the parallel lines are equal.

The formula used: The slope of the line, m = \(\frac{y_2-y_1}{x_2-x_1}\)

Now, The slope of AB = \(\frac{1-(-3)}{-5-2}\)

The Slope of AB = \(\frac{4}{-7}\)

Now, The slope of CD = \(\frac{3-(-1)}{0-7}\)

The Slope of AB = \(\frac{4}{-7}\)

So, The slope of AB = The slope of CD

Hence, The given Lines are parallel to each other.