Question 1177514: Triangle ABC has its coordinate at A(a,-1),B(8,-1) and C(5,4).If the base is twice the height, find a.
Found 2 solutions by ikleyn, MathLover1:
Answer by ikleyn(52781)   (Show Source):
You can put this solution on YOUR website! .
The problem does not disclose which of the three sides of the triangle is called "the base";
so I will assume that the base is the horizontal segment AB.
Then the length of the base is |8-a| units, while the height is 4 - (-1) = 5 units.
We find "a" from this absolute value equation
| 8-a | = 2*5,
which is equivalent to
| a-8 | = 10.
It has two solutions a= 18 or a= -2.
ANSWER. Possible values of "a" are -2 or 18.
Solved, answered, explained and completed.
////////////
Notice that @Mathlover1 LOST other possible solution a= 18.
So, her solution is not complete.
Answer by MathLover1(20849)  (Show Source):
You can put this solution on YOUR website! A( , ),
B( ,) and => both have same y coordinate, so both lie on  line
C( , )-> since A and B lie on  line, distance from line to point C is units; so, the height of triangle is
If the base is  the height, base is  units long
from B(,) go units to the left and you will get to  which is
so, and point A is at (,)
|
|
|
