What is the perpendicular bisector of a line with points at A $(-33, 7.5)$ and B $(4,17)$ ?

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Answer 1 · 2016-03-11T08:54:55

Equation of perpendicular bisector is $296x+76y+3361=0$

Let us use point slope form of equation, as the desired line passes through mid point of A $(-33,7.5)$ and B $(4,17)$ .

This is given by $((-33+4)/2,(7.5+17)/2)$ or $(-29/2,49/4)$

The slope of line joining A $(-33,7.5)$ and B $(4,17)$ is $(17-7.5)/(4-(-33))$ or $9.5/37$ or $19/74$ .

Hence slope of line perpendicular to this will be $-74/19$ , (as product of slopes of two perpendicular lines is $-1$ )

Hence perpendicular bisector will pass through $(-29/2,49/4)$ and will have a slope of $-74/19$ . Its equation will be

$y-49/4=-74/19(x+29/2)$ . To simplify this multiply all by $76$ , LCM of the denominators $2,4,19$ . Then this equation becomes

$76y-49/4xx76=-74/19xx76(x+29/2)$ or

$76y-931=-296x-4292$ or $296x+76y+3361=0$

What is the perpendicular bisector of a line with points at A (-33, 7.5)(-33, 7.5) and B (4,17)(4,17)?