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4th Edition

James Stewart

Publisher: Cengage Learning

ISBN: 9781337687805

Chapter T, Problem 4BDT

(a)

To determine

**To find:** The slope of the line that contains

Expert Solution

The slope of the line is

**Formula used:**

The slope of the line is

**Calculation:**

It is given that the line that contains

Substitute

Thus, the slope of the line is

(b)

To determine

**To find:** The equation and the intercept of the line that contains

Expert Solution

The intercept of the line is

**Given:**

The slope of the line is

**Formula used:**

The equation of the straight line is
*m* is the slope of the line, *c* is the *x*-intercept.

**Calculation:**

Suppose, the equation of the straight line is

It is given that, the slope of the line is

Thus, substitute

It is given that, the line passes through the point

Thus, substitute

Thus, the value is

Thus, substitute

Thus, the intercept of the line is

(c)

To determine

**To find:** The mid points of the points

Expert Solution

The midpoint of the points

**Formula used:**

The midpoint of the points

**Calculation:**

It is given that the points are

Substitute

Thus, the midpoint of the points

(d)

To determine

**To find:** The length of the segment between the points

Expert Solution

The length of the segment between the points

**Formula used:**

The length of the segment between the points

**Calculation:**

It is given that the points are

Substitute

Length cannot be any negative term. Thus, the length is 20.

Thus, the length of the segment between the points

(e)

To determine

**To find:** The equation of the perpendicular bisector of *AB*.

Expert Solution

The equation of the perpendicular bisector is

**Given:**

The points are

The slope of the line *AB* is

The midpoint of the points

**Formula used:**

The equation of the straight line is
*m* is the slope of the line, *c* is the *x*-intercept.

**Calculation:**

Suppose, the equation of the straight line is

It is given that, the slope of the line *AB* is

Thus, slope of the perpendicular bisector of *AB* is

Thus, substitute

It is given that, the line passes through the midpoint, that is

Thus, substitute

Thus, the value is

Thus, substitute

Thus, the equation of the perpendicular bisector is

(f)

To determine

**To find:** The equation of the circle that has diameter as *AB*.

Expert Solution

The equation of the circle is

**Given:**

The points are

The midpoint of the points

The length of the segment between the points

**Formula used:**

The equation of the circle is
*r* is the radius of the circle.

**Calculation:**

Suppose, the equation of the circle is

It is given that, the center of the circle is at the midpoint of the points

Thus, substitute

The radius is the half of the length of the segment *AB*.

It is given that the length of the segment between the points

Thus, the radius is

Thus, substitute

Thus, the equation of the circle is