The vertices of triangle ABC are A(-4,0), B(2,4), and C(4,0). What is its area?

Answer 1

#16un.^2#

Don"t be intimidated by the points. Graph them and find your base and height

This is easy because your base is just the distance from A to A on the horizontal plane, 8. The height is defined by the vertical distance of B, 4.

Now use the area of a triangle formula (A = #1/2*b*h#) A = #1/2(4)(8)# A = #1/2 * 32# A = 16

Your area is 16 sq. units.

Sign up to view the whole answer

By signing up, you agree to our Terms of Service and Privacy Policy

Sign up with email
Answer 2

# 16" sq. units."#

Let us denote, by #[ABC],# the Area of a #DeltaABC.#

We know from the Co-ordinate Geometry, that, if the vertices of

#DeltaABC# are #A(x_1,y_1), B(x_2,y_2), and, C(x_3,y_3),# then,
#[ABC]=1/2*|D|," where, "D=|(x_1,y_1,1),(x_2,y_2,1),(x_3,y_3,1)|.#
Here, #D=|(-4,0,1),(2,4,1),(4,0,1)|,#
#=-4(4xx1-0xx1)-0+1(2xx0-4xx4),#
#=-4(4)+1(-4),#
# rArr D=-32.#
#"Therefore, "[ABC]=1/2*|-32|=16" sq.units."#
Sign up to view the whole answer

By signing up, you agree to our Terms of Service and Privacy Policy

Sign up with email
Answer 3

To find the area of triangle ABC with vertices A(-4,0), B(2,4), and C(4,0), you can use the formula for the area of a triangle given its vertices. One common method is using the formula:

[Area = \frac{1}{2} |x_1(y_2 - y_3) + x_2(y_3 - y_1) + x_3(y_1 - y_2)|]

Substituting the coordinates of points A, B, and C into this formula:

[Area = \frac{1}{2} |-4(4 - 0) + 2(0 - 4) + 4(4 - 0)|]

[= \frac{1}{2} |-16 + (-8) + 16|]

[= \frac{1}{2} |-16 - 8 + 16|]

[= \frac{1}{2} |-8|]

[= \frac{1}{2} \times 8]

[= 4]

Therefore, the area of triangle ABC is 4 square units.

Sign up to view the whole answer

By signing up, you agree to our Terms of Service and Privacy Policy

Sign up with email
Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

Not the question you need?

Drag image here or click to upload

Or press Ctrl + V to paste
Answer Background
HIX Tutor
Solve ANY homework problem with a smart AI
  • 98% accuracy study help
  • Covers math, physics, chemistry, biology, and more
  • Step-by-step, in-depth guides
  • Readily available 24/7