What is the area of a triangle whose vertices are the points with coordinates (3,2) (5,10) and (8,4)?

Answer 1

Refer to explanation

first remedy

We can use Heron formula which states

The area of a triangle with sides a,b,c is equal to

#S=sqrt(s(s-a)(s-b)(s-c))# where #s=(a+b+c)/2#
No using the formula to find the distance between two points #A(x_A,y_A) , B(x_B,y_B)#which is
#(AB)=sqrt((x_A-x_B)^2+(y_A-y_B)^2#
we can calculate the length of sides between the three points given let say #A(3,2)# #B(5,10)# , #C(8,4)#

After that, we substitute to Heron formula.

2nd Solution

We know that if #(x_1,y_1), (x_2,y_2)# and #(x_3,y_3)# are the vertices of the triangle, then the area of the triangle is given by:
Area of the triangle# = (1/2) |{(x2-x1)(y2+y1) +(x3-x2)(y3+y1)+(x1-x3)(y1+y2)}|#
Therefore the area of the triangle whose vertices are #(3,2), (5,10), (8 ,4)# is given by:
Area of the triangle# = (1/2) |{(5-3)(10+2) +(8-5)(4+2)+(3-8)(2+10)}|=abs(1/2(24+18-60))=9#
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Answer 2

#18#

Method 1: Geometric

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Answer 3

To find the area of the triangle formed by the given vertices, you can use the formula for the area of a triangle given its coordinates.

Let's label the vertices A(3,2), B(5,10), and C(8,4).

Then, you can use the formula:

Area = |(x1(y2-y3) + x2(y3-y1) + x3(y1-y2))/2|

Substitute the coordinates of the vertices into the formula:

Area = |(3(10-4) + 5(4-2) + 8(2-10))/2|

Calculate the expression:

Area = |(3(6) + 5(2) + 8(-8))/2|

Area = |(18 + 10 - 64)/2|

Area = |(-36)/2|

Area = |-18|

So, the area of the triangle formed by the given vertices is 18 square units.

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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.

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