Question

the coordinates of the vertices of a triangle are (3,-7/2),(7/2,-1) and (5/2,3/2) show that area of the triangle is 15/8 square units.
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Answer 1

Answer:

No idea at all

Step-by-step explanation:

sorry not able to answer at all

Answer 2

Area of triangle is $\frac{15}{8}$ square units

Given: Coordinates of triangle are  (3,-7/2),(7/2,-1) and (5/2,3/2)

To Find: We need to if the area of triangle is 15/8 square units.

Solution:

As we know area of triangle with vertices (x₁, x₂), (x₂, y₂) and (x₃, y₃) is given by  = $\frac{1}{2} | x_{1} (y_{2}- y_{3} ) + x_{2} (y_{3} -y_{1} ) + x_{3} (y_{1} -y_{2} ) |$  

From given data area of triangle

=   $\frac{1}{2} | 3 (-1- \frac{3}{2} ) +\frac{7}{2} (\frac{3}{2} -(-\frac{7}{2} )) + \frac{5}{2} (-\frac{7}{2} - (-1) ) |$  

=   $\frac{1}{2} | 3 (-1- \frac{3}{2} ) +\frac{7}{2} (\frac{3}{2} +\frac{7}{2} )) + \frac{5}{2} (-\frac{7}{2} +1) |$

=  $\frac{1}{2} | 3 ( \frac{-2-3}{2} ) +\frac{7}{2} (\frac{10}{2} ) + \frac{5}{2} (\frac{-7+2}{2} ) |$

=  $\frac{1}{2} | 3 ( \frac{-5}{2} ) +\frac{7}{2} (5)+ \frac{5}{2} (\frac{-5}{2} ) |$

=  $\frac{1}{2} | \frac{-15}{2} +\frac{35}{2} + \frac{-25}{4} |$      

=  $\frac{1}{2} | \frac{(-15)(2) + 35(2)-25}{4} }{ |$

=  $\frac{1}{2} | \frac{- 30 + 70-25}{4} }{ |$

=  $\frac{1}{2} | \frac{-15}{4} }{ |$ = $\frac{15}{8}$  square units

Hence, it is proven that area of triangle = $\frac{15}{8}$ square units

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