Question

Points A(9,2), B(5,6), and C(-3, - 2) are given. The distance between point and

the perpendicular bisector of AB is:

Answer 1

Answer:

Step-by-step explanation:

Answer 2

The distance between point and the perpendicular bisector of AB is 2√2.

At which point does the perpendicular bisector?

• A perpendicular bisector is a line that cuts a line segment connecting two points exactly in half at a 90 degree angle.
• To find the perpendicular bisector of two points, all you need to do is find their midpoint and negative reciprocal, and plug these answers into the equation for a line in slope-intercept form.

How do I find the equation of a perpendicular line?

• Perpendicular lines have opposite-reciprocal slopes, so the slope of the line we want to find is 1/2.
• Plugging in the point given into the equation y = 1/2x + b and solving for b, we get b = 6.
• Thus, the equation of the line is y = ½x + 6. Rearranged, it is –x/2 + y = 6.

According to the question:

6–2/5–9.

4/—4.

-1 = slope.

The slope of perpendicular bisector would be,

-1/slope.

= 1 (slope of perpendicular bisector).

Now, the mid point of A and B lies on the perpendicular bisector.

= ( 7,4) lies on perpendicular bisector.

Equation of perpendicular bisector.

= Y-4 / X-7 = 1.

Y-4 = X-7.

Y-X + 3 = 0.

Now using the formula for calculating the distance of C from the perpendicular bisector,

C(-3,-2).

-3(-1) + (-2)(1) + 3/√2.

3-2 + 3/√2.

4 /√2.

2√2 ( distance of C from perpendicular bisector)

Hence, The distance between point and the perpendicular bisector of AB is 2√2.

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