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6th Edition

Stewart + 5 others

Publisher: Cengage Learning

ISBN: 9780840068071

Chapter 1, Problem 17T

(a)

To determine

**To sketch:** The points *P* and *Q* in the coordinate plane.

Expert Solution

The given points is

In point
*x*-coordinate is negative and *y*-coordinate is positive, so it is lies on II Quadrant and point

The coordinate plane of two given points is shown below,

Figure (1)

Figure (1) shows the points

(b)

To determine

**To find:** The distance between

Expert Solution

The distance between *P* and *Q* is

**Given:**

The points is

**Calculation:**

The distance formula of two points

Where,

Substitute 5 for

Thus, the distance between *P* and *Q* is

(c)

To determine

**To find:** The midpoint of line segment *PQ*.

Expert Solution

The midpoint of segment *PQ* is

**Given:**

The points is

**Calculation:**

The formula of line segment from

Substitute 5 for

Thus, the midpoint of segment *PQ* is

(d)

To determine

**To find:** The slope of line passes through two pints *P* and *Q*.

Expert Solution

The slope of line *PQ* is

**Given:**

The points is

**Calculation:**

The formula of slope of line passes through two points is,

In above formula *m* is slope of line and

Substitute 6 for

Thus, the slope of line *PQ* is

(e)

To determine

**To find:** The perpendicular bisector of line *PQ*.

Expert Solution

The equation of perpendicular bisector is

**Given:**

The points is

**Calculation:**

The slope of line passes through points

The lines are perpendicular if,

Where,

Substitute

The slope
*PQ* and perpendicular bisector is a line passes midpoint
*PQ* obtained from part (c) with slope

The formula of point-slope form of line is,

Substitute
*m*in the above formula to get equation of perpendicular bisector,

Thus, the equation of perpendicular bisector is

(f)

To determine

**To find:** The equation of circle with diameter *PQ*.

Expert Solution

The equation of circle is

**Given:**

The points is
*PQ* is a diameter of circle.

**Calculation:**

The equation of circle with center
*r* is,

The distance between points

The radius of circle is half of diameter that is,

The line segment *PQ* is a diameter of circle and the midpoint of line segment *PQ* is center of circle that is

Substitute 1 for *h*,
*k* and
*r* in equation (1) to get the equation of circle,

Thus, the equation of circle is