CameraIcon
CameraIcon
SearchIcon
MyQuestionIcon


Question

Check whether $$(5, -2),(6,4)$$ and $$(7,-2)$$ are the vertices of an isosceles triangle.


Solution

The vertices of a triangle ABC is given as $$A\left( {5, - 2} \right)$$, $$B\left( {6,4} \right)$$ and $$C\left( {7, - 2} \right)$$.

The distance AB is,

$$AB = \sqrt {{{\left( {6 - 5} \right)}^2} + {{\left( {4 - \left( { - 2} \right)} \right)}^2}} $$

$$ = \sqrt {{{\left( 1 \right)}^2} + {{\left( 6 \right)}^2}} $$

$$ = \sqrt {1 + 36} $$

$$ = \sqrt {37} $$

The distance BC is,

$$BC = \sqrt {{{\left( {7 - 6} \right)}^2} + {{\left( { - 2 - 4} \right)}^2}} $$

$$ = \sqrt {{{\left( 1 \right)}^2} + {{\left( { - 6} \right)}^2}} $$

$$ = \sqrt {1 + 36} $$

$$ = \sqrt {37} $$

The distance CA is,

$$CA = \sqrt {{{\left( {5 - 7} \right)}^2} + {{\left( { - 2 - \left( { - 2} \right)} \right)}^2}} $$

$$ = \sqrt {{{\left( { - 2} \right)}^2} + 0} $$

$$ = \sqrt 4 $$

$$ = 2$$

Since, $$AB = BC$$, that is the two sides of a triangle are equal, therefore, the triangle is an isosceles triangle.


Mathematics

Suggest Corrections
thumbs-up
 
0


similar_icon
Similar questions
View More


similar_icon
People also searched for
View More



footer-image