Question

if A (4,-2) , B (7,9) , C (7,-2) are the vertices of a ️abc , then the ️ABC is
(a) equilateral triangle
(b) isosceles triangle
(c) right angled triangle
(d) isosceles right angled triangle

explain please​

Answer 1

Answer:

right angled triangle

THANK YOU

Answer 2

(c) Right angled triangle

Here, according to the given information, we are given that,

The points of the triangle are, A (4,-2) , B (7,9) , C (7,-2).

Now, in order to check if the triangle is an equilateral triangle, an isosceles triangle, an isosceles right angled triangle or a right angled triangle, we need to find the distance between the points to confirm about the sides of the triangles first.

Now, distance between A and B is AB =

$\sqrt{(7-4)^{2} +(9+2)^{2} } \\=\sqrt{9+121} \\=\sqrt{130} \\=11.4$

Again, proceeding in a similar way, distance between B and C is BC =

$\sqrt{(-2-9)^{2} +(7-7)^{2} } \\=11$

Again, proceeding in a similar way, distance between A and C is AC =

$\sqrt{(-2+2)^{2} +(7-4)^{2} } \\=3$

Now, applying pythagoras theorem, we get,

$AB^{2} +BC^{2} \\=130$

Which is equal to $AC^{2}$.

Hence, option c is correct.

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