SOLUTION: The vertices of a triangle are at A(-3, -2), B(2, 1) and C(6, 5). Find the length of the altitude from the vertex C and the length of side AB. Then compute for the area of the tr

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Question 1189504: The vertices of a triangle are at A(-3, -2), B(2, 1) and C(6, 5). Find the length of the altitude
from the vertex C and the length of side AB. Then compute for the area of the triangle.

Found 2 solutions by MathLover1, greenestamps:
Answer by MathLover1(20849)   (Show Source): You can put this solution on YOUR website!
The vertices of a triangle are at
A(, )
B(, )
C(, )

the length of side AB or is equal to the distance between A and B




height to lie on a line perpendicular to AB and passes through C
use coordinates of A and B first to find a slope of the line passing through A and B



then line is
........use slope and (, )




then, a line to AB will be

.......use slope and (, )




find intersection point
...solving it, you get




convert to decimal:
,

height is distance between C and intersection point




Area:
if and , the area will be


square units




Answer by greenestamps(13200)   (Show Source): You can put this solution on YOUR website!


Use the Pythagorean Formula (aka distance formula) to find the length of AB:




The length of the altitude to AB is the distance of the point (6,5) from the line containing AB.

Use the coordinates of A and B to determine that the equation of AB can be written as .

The distance of the point (p,q) from the line Ax+By+C=0 is given by the formula









Then the area of the triangle is one-half base times height:




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