What is the volume of this pyramid
1 answer:
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Answer:
coordinates of its centroid=(-1,-1)
Step-by-step explanation:
The given three lines are:
8x+3y=12, (1)
6y-7x=24 (2)
and x+9y+33. (3)
Multiplying equation (1) by 2 and subtract the equation (2), we get
23x=0⇒x=0,
Putting the value of x=0 in equation (2), we get
6y=24
y=4
Now, multiply the first equation by 3 and subtract the equation (3), we get
23x=69⇒x=3
Putting the value of x=3 in equation (1), we get
24+3y=12
3y=-12
y=-4
Also, multiplying the equation (3) by 7 and add the equation (2), we get
69y=-207
y=-3
Putting the value of y=-3 in equation (2), we get
6(-3)-7x=24
-18-24=7x
x=-6
So the centroid is located at (the average of the three vertices):
and
.
Thus, the coordinates of its centroid=(-1,-1)