Geometry For Enjoyment And Challenge
Geometry For Enjoyment And Challenge
91st Edition
ISBN: 9780866099653
Author: Richard Rhoad, George Milauskas, Robert Whipple
Publisher: McDougal Littell
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Chapter 15, Problem 11CR

a.

To determine

To find the lengths and the slopes of AB, BC and AC.

a.

Expert Solution
Check Mark

Answer to Problem 11CR

  13,14,15

Explanation of Solution

Given:

The given triangle ABC with vertices A(3,8),B(8,−4) and C(−6,−4) .

Calculation:

Calculating the lengths of AB, BC and AC as follows-

  AB=(3−8)2+(8+4)2=25+144=13BC=(8+6)2+(−4+4)2=142=14AC=(3+6)2+(8+4)2=81+144=15

b.

To determine

To find the type of triangle.

b.

Expert Solution
Check Mark

Answer to Problem 11CR

Acute.

Explanation of Solution

Given:

The given triangle ABC with vertices A(3,8),B(8,−4) and C(−6,−4) .

Calculation:

Since from part (a) all the sides are different, the triangle is acute.

c.

To determine

To find the equation of AC and its x and y intercepts.

c.

Expert Solution
Check Mark

Answer to Problem 11CR

  y=43x+4

Explanation of Solution

Given:

The given triangle ABC with vertices A(3,8),B(8,−4) and C(−6,−4) .

Calculation:

The equation of AC is

  y−y1=y2−y1x2−x1(x−x1)y−8=−4−8−6−3(x−3)y−8=43(x−3)y=43x+4

d.

To determine

To find the equation of BC.

d.

Expert Solution
Check Mark

Answer to Problem 11CR

  y=−4

Explanation of Solution

Given:

The given triangle ABC with vertices A(3,8),B(8,−4) and C(−6,−4) .

Calculation:

The equation of BC is

  y−y1=y2−y1x2−x1(x−x1)y+4=−4+4−6−8(x−8)y+4=0y=−4

e.

To determine

To find where does the altitude BC intersect BC.

e.

Expert Solution
Check Mark

Explanation of Solution

Given:

The given triangle ABC with vertices A(3,8),B(8,−4) and C(−6,−4) .

Calculation:

Calculating the lengths of AB, BC and AC as follows-

  AB=(3−8)2+(8+4)2=25+144=13BC=(8+6)2+(−4+4)2=142=14AC=(3+6)2+(8+4)2=81+144=15

f.

To determine

To find the equation of BC.

  y=−4

Given:

The given triangle ABC with vertices A(3,8),B(8,−4) and C(−6,−4) .

Calculation:

The equation of BC is

  y−y1=y2−y1x2−x1(x−x1)y+4=−4+4−6−8(x−8)y+4=0y=−4

f.

Expert Solution
Check Mark

Answer to Problem 11CR

  y=−4

Explanation of Solution

Given:

The given triangle ABC with vertices A(3,8),B(8,−4) and C(−6,−4) .

Calculation:

The equation of BC is

  y−y1=y2−y1x2−x1(x−x1)y+4=−4+4−6−8(x−8)y+4=0y=−4

g.

To determine

To find the lengths of altitude to BC.

g.

Expert Solution
Check Mark

Answer to Problem 11CR

  12

Explanation of Solution

Given:

The given triangle ABC with vertices A(3,8),B(8,−4) and C(−6,−4) .

Calculation:

The length of altitude to BC is 12 .

h.

To determine

To find the midpoint of CB and the slope of the median to CB.

h.

Expert Solution
Check Mark

Answer to Problem 11CR

  (1,−4)

Explanation of Solution

Given:

The given triangle ABC with vertices A(3,8),B(8,−4) and C(−6,−4) .

Calculation:

The midpoint of CB is

  (8−62,−4−42)=(1,−4)

i.

To determine

To find the area of triangle ABC,

i.

Expert Solution
Check Mark

Answer to Problem 11CR

  84

Explanation of Solution

Given:

The given triangle ABC with vertices A(3,8),B(8,−4) and C(−6,−4) .

Calculation:

The area of triangle ABC is-

  absinc2=84

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Chapter 15, Problem 10CR
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Chapter 15, Problem 12CR

Chapter 15 Solutions

Geometry For Enjoyment And Challenge

Ch. 15.1 - Prob. 1PSACh. 15.1 - Prob. 2PSACh. 15.1 - Prob. 3PSACh. 15.1 - Prob. 4PSACh. 15.1 - Prob. 5PSACh. 15.1 - Prob. 6PSACh. 15.1 - Prob. 7PSBCh. 15.1 - Prob. 8PSBCh. 15.1 - Prob. 9PSBCh. 15.1 - Prob. 10PSB
Ch. 15.1 - Prob. 11PSBCh. 15.1 - Prob. 12PSBCh. 15.1 - Prob. 13PSBCh. 15.1 - Prob. 14PSCCh. 15.1 - Prob. 15PSCCh. 15.1 - Prob. 16PSCCh. 15.1 - Prob. 17PSCCh. 15.1 - Prob. 18PSCCh. 15.1 - Prob. 19PSCCh. 15.1 - Prob. 20PSDCh. 15.2 - Prob. 1PSACh. 15.2 - Prob. 2PSACh. 15.2 - Prob. 3PSACh. 15.2 - Prob. 4PSACh. 15.2 - Prob. 5PSACh. 15.2 - Prob. 6PSACh. 15.2 - Prob. 7PSBCh. 15.2 - Prob. 8PSBCh. 15.2 - Prob. 9PSBCh. 15.2 - Prob. 10PSBCh. 15.2 - Prob. 11PSBCh. 15.2 - Prob. 12PSBCh. 15.2 - Prob. 13PSBCh. 15.2 - Prob. 14PSBCh. 15.2 - Prob. 15PSBCh. 15.2 - Prob. 16PSBCh. 15.2 - Prob. 17PSBCh. 15.2 - Prob. 18PSBCh. 15.2 - Prob. 19PSBCh. 15.2 - Prob. 20PSCCh. 15.2 - Prob. 21PSCCh. 15.2 - Prob. 22PSCCh. 15.2 - Prob. 23PSCCh. 15.2 - Prob. 24PSCCh. 15.2 - Prob. 25PSCCh. 15.3 - Prob. 1PSACh. 15.3 - Prob. 2PSACh. 15.3 - Prob. 3PSACh. 15.3 - Prob. 4PSACh. 15.3 - Prob. 5PSACh. 15.3 - Prob. 6PSACh. 15.3 - Prob. 7PSACh. 15.3 - Prob. 8PSBCh. 15.3 - Prob. 9PSBCh. 15.3 - Prob. 10PSBCh. 15.3 - Prob. 11PSBCh. 15.3 - Prob. 12PSBCh. 15.3 - Prob. 13PSBCh. 15.3 - Prob. 14PSBCh. 15.3 - Prob. 15PSBCh. 15.3 - Prob. 16PSBCh. 15.3 - Prob. 17PSBCh. 15.3 - Prob. 18PSBCh. 15.3 - Prob. 19PSBCh. 15.3 - Prob. 20PSCCh. 15.3 - Prob. 21PSCCh. 15.3 - Prob. 22PSCCh. 15.3 - Prob. 23PSCCh. 15.3 - Prob. 24PSCCh. 15.3 - Prob. 25PSCCh. 15.3 - Prob. 26PSCCh. 15 - Prob. 1RPCh. 15 - Prob. 2RPCh. 15 - Prob. 3RPCh. 15 - Prob. 4RPCh. 15 - Prob. 5RPCh. 15 - Prob. 6RPCh. 15 - Prob. 7RPCh. 15 - Prob. 8RPCh. 15 - Prob. 9RPCh. 15 - Prob. 10RPCh. 15 - Prob. 11RPCh. 15 - Prob. 12RPCh. 15 - Prob. 13RPCh. 15 - Prob. 14RPCh. 15 - Prob. 15RPCh. 15 - Prob. 16RPCh. 15 - Prob. 17RPCh. 15 - Prob. 18RPCh. 15 - Prob. 19RPCh. 15 - Prob. 20RPCh. 15 - Prob. 21RPCh. 15 - Prob. 22RPCh. 15 - Prob. 23RPCh. 15 - Prob. 24RPCh. 15 - Prob. 25RPCh. 15 - Prob. 1CRCh. 15 - Prob. 2CRCh. 15 - Prob. 3CRCh. 15 - Prob. 4CRCh. 15 - Prob. 5CRCh. 15 - Prob. 6CRCh. 15 - Prob. 7CRCh. 15 - Prob. 8CRCh. 15 - Prob. 9CRCh. 15 - Prob. 10CRCh. 15 - Prob. 11CRCh. 15 - Prob. 12CRCh. 15 - Prob. 13CRCh. 15 - Prob. 14CRCh. 15 - Prob. 15CRCh. 15 - Prob. 16CRCh. 15 - Prob. 17CRCh. 15 - Prob. 18CRCh. 15 - Prob. 19CRCh. 15 - Prob. 20CRCh. 15 - Prob. 21CRCh. 15 - Prob. 22CRCh. 15 - Prob. 23CRCh. 15 - Prob. 24CRCh. 15 - Prob. 25CRCh. 15 - Prob. 26CRCh. 15 - Prob. 27CRCh. 15 - Prob. 28CRCh. 15 - Prob. 29CRCh. 15 - Prob. 30CRCh. 15 - Prob. 31CRCh. 15 - Prob. 32CRCh. 15 - Prob. 33CRCh. 15 - Prob. 34CRCh. 15 - Prob. 35CRCh. 15 - Prob. 36CRCh. 15 - Prob. 37CRCh. 15 - Prob. 38CRCh. 15 - Prob. 39CRCh. 15 - Prob. 40CRCh. 15 - Prob. 41CRCh. 15 - Prob. 42CRCh. 15 - Prob. 43CRCh. 15 - Prob. 44CRCh. 15 - Prob. 45CRCh. 15 - Prob. 46CRCh. 15 - Prob. 47CRCh. 15 - Prob. 48CRCh. 15 - Prob. 49CRCh. 15 - Prob. 50CR

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