Answer

Verified

403.2k+ views

**Hint:**

A triangle with vertices at $(x_1,y_1)$, $(x_2,y_2)$, and $(x_3,y_3)$. If the triangle was a right-angled triangle, it would be pretty easy to compute the area of a triangle by finding one-half the product of the base and the height (area of triangle formula). However, when the triangle is not a right-angled triangle there are multiple different ways to do so. It turns out that the area of triangle formula can also be found using determinants.

Area of triangle \[ = \dfrac{1}{2} \times \left| {\begin{array}{*{20}{c}}{x_1}&{y_1}&1\\{x_2}&{y_2}&1\\{x_3}&{y_3}&1\end{array}} \right|\]

**Complete step by step solution:**

Let any point on the line \[x - y = 2\] be \[C = (h,h - 2)\]

Coordinate of vertex \[A = ( - 5,0)\]

Coordinate of vertex \[B = (3,0)\]

Area of ..

\[\begin{array}{l} \Rightarrow \dfrac{1}{2} \times \left| {\begin{array}{*{20}{c}}h&{h - 2}&1\\{ - 5}&0&1\\3&0&1\end{array}} \right| = 20\\ \Rightarrow 8(h - 2) = 40\\ \Rightarrow h - 2 = \pm 5\\ \Rightarrow h = 7or - 3\end{array}\]

Hence, the points are (7, 5) and (-3, -5).

**So, Option B and D are correct.**

**Note:**

In order to find the area of a triangle, one must multiply the base by the height. Afterward, one must divide it by 2. The division by 2 comes because one can divide a parallelogram into 2 triangles.

In order to find the area of any right triangle, multiplication of the lengths of the two sides must take place. These two sides are perpendicular to each other. Afterward, one must take half of that.

A scalene triangle is one which has all three sides of different lengths. The area of a scalene triangle that has a base b and height h is given by 1/2 bh. If one knows the lengths of all three sides, one can find the area by making use of the Heron’s Formula without the need to find the height.

Recently Updated Pages

The base of a right prism is a pentagon whose sides class 10 maths CBSE

A die is thrown Find the probability that the number class 10 maths CBSE

A mans age is six times the age of his son In six years class 10 maths CBSE

A started a business with Rs 21000 and is joined afterwards class 10 maths CBSE

Aasifbhai bought a refrigerator at Rs 10000 After some class 10 maths CBSE

Give a brief history of the mathematician Pythagoras class 10 maths CBSE

Trending doubts

Difference Between Plant Cell and Animal Cell

Give 10 examples for herbs , shrubs , climbers , creepers

Name 10 Living and Non living things class 9 biology CBSE

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

Fill the blanks with the suitable prepositions 1 The class 9 english CBSE

Change the following sentences into negative and interrogative class 10 english CBSE

Write a letter to the principal requesting him to grant class 10 english CBSE

Fill the blanks with proper collective nouns 1 A of class 10 english CBSE

Write the 6 fundamental rights of India and explain in detail