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The coordinates of point D are (7, 4) and the coordinates of point E are (1, −3) .

What is the slope of the line that is perpendicular to DE¯¯¯¯¯?



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ANSWER

[tex]- \frac{6}{7} [/tex]

EXPLANATION

The given points are

[tex](x_1,y_1)=(7,4)[/tex]
and

[tex](x_2,y_2)=(1,-3)[/tex]

The formula for finding the slope is given by,

[tex]slope = \frac{y_1-y_1}{x_1-x_1} [/tex]

We substitute the points to obtain,

[tex]slope = \frac{ - 3 - 4}{1 - 7} = \frac{7}{6} [/tex]

The slope of the line that is perpendicular to DE is the negative reciprocal of

[tex]\frac{7}{6} [/tex]

Thus, the line perpendicular to DE has slope,

[tex] \frac{ - 1}{ \frac{ 7}{6} } =-\frac{6}{7} [/tex]

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