Find Coordinates & Area of Triangles with Math Functions

[Peter G.]

The graph of function f (x) 3x - 4 intersects the x-axis at point A and the y-axis at point B.

Find the coordinates of:
a)

i) A
ii) B

b) Let O denote the origin, find the area of triangle OAB

So my answers:

i) 0 = 3x - 4
3x = 4
x = 4/3

Coordinates: (4/3,0)

ii) (0, -4)

so, for b: b x h / 2:
(-4 x 4/3) / 2
= - 8 / 3

But the book says it is: 8/3 √x - 4 + 3

Any help please?

Thanks,
Peter G.

 

[HallsofIvy]

The graph of function f (x) 3x - 4 intersects the x-axis at point A and the y-axis at point B.

Find the coordinates of:
a)

i) A
ii) B

b) Let O denote the origin, find the area of triangle OAB

So my answers:

i) 0 = 3x - 4
3x = 4
x = 4/3

Coordinates: (4/3,0)

ii) (0, -4)

so, for b: b x h / 2:
(-4 x 4/3) / 2
= 8 / 3

But the book says it is: 8/3 √x - 4 + 3

Any help please?

Thanks,
Peter G.

Are you sure you have copied the problem correctly? y= 3x- 4 is a single line that intesects the x and y axes at specific points. The area of the triangle must be a number, not a function of x. Perhaps you are accidently looking at the book's answer to a different problem.

 

[Peter G.]

I think the book has been misprinted. Question 6 has questions a (i) and (ii) and b. Question 7 has questions a, b and c.

At the back of the book, question 7 has answers a and c, not b. The answer I got for 7 b was: √x - 4 + 3, which is put as part of answer 6 b.

So I think I settled that issue, but, I got as an answer negative 8/3 and the book has positive 8/3. Which one do you think is right?

 

[eumyang]

So I think I settled that issue, but, I got as an answer negative 8/3 and the book has positive 8/3. Which one do you think is right?

It's positive. b should have been 4, not -4. The length of b is the distance from O (0, 0) to B (0, -4), and distances are positive, hence the positive 4.

 

[ProPM]

Ok, thanks.