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a A Straight line passes through A(-2,1) and B(2,-k). The
line is perpendicular to a line 3y+2x=5 . determine k
​

Sagot :

Given :

A Straight line passes through A(-2,1) and B(2,-k).

The  line is perpendicular to a line 3y+2x=5 .

To Find :

The value of k.

Solution :

Let, slope of line is m.

We know, product of slope of in straight line is -1.

[tex]m \times \dfrac{-2}{3} = -1\\\\m = \dfrac{3}{2}[/tex]

We know, slope is given by :

[tex]\dfrac{y_2-y_1}{x_2-x_1} = \dfrac{3}{2}\\\\\dfrac{1-(-k)}{-2 - 2} = \dfrac{3}{2}\\\\\dfrac{1+k}{-4} = \dfrac{3}{2}\\\\k = -7[/tex]

Therefore, the value of k is -7.

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