Question

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

Answer 1

Step-by-step explanation:

if both line are parallel then their slope must be equal ..

formula of finding slope from given coordinates are ..y2 -y1 / x2 - x1

now , slope of first line = slope of second line

1 -(-3) /-5 - 2 = 3-(-1) /0 -7

-4/7 = -4/7

proved

Answer 2

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

Solution:

For two lines to be parallel, their slopes must be equal

The slope of a line is given as:

$m = \frac{y_2-y_1}{x_2-x_1}$

Find slope of line joining (2, -3) and (-5, 1)

$(x_1, y_1) = (2, -3)\\\\(x_2, y_2) = (-5, 1)$

Therefore,

$m = \frac{1+3}{-5-2}\\\\m = \frac{4}{-7}\\\\m = \frac{-4}{7}$

Find slope of line joining (7, -1) and (0, 3)

$(x_1, y_1) = (7,-1)\\\\(x_2, y_2) = (0,3)$

Therefore,

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

Thus, both the slopes are same

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

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