The points (- 4,0), (4, 0) and (0,3) are the vertices of a/ana)right triangleb)isosceles trianglec)equilateral triangled)scalene triangleCorrect answer is option 'B'. Can you explain this answer?

Question

Answer

Let X (- 4, 0), Y (4, 0) and Z(0, 3) are the given vertices.

Now, distance between X( - 4, 0) and Y(4, 0),

⇒ XY = √[4 - (- 4)]� + (0 - 0)�

⇒ XY = √(4 - 4)�

⇒ XY = √(8)�

⇒ XY = 8

Distance between Y(4, 0) and Z(0, 3),

⇒ YZ = √(0 - 4)� + (3 - 0)�

⇒ YZ = √16 + 9

⇒ YZ = √25

⇒ YZ = 5

Distance between Z(4, 0) and X(0, 3)

⇒ ZX = √[0 - (- 4)]� + (3 - 0)�

⇒ ZX = √16 + 9

⇒ ZX = √25

⇒ ZX = 5

As, YZ = ZX

Two sides of the triangle are equal.

So that, the triangle XYZ is an isosceles triangle.

Answer

Answer

Isosceles Triangle
To determine the type of triangle formed by the given points, we need to analyze the lengths of the sides of the triangle.

Calculating the Length of Sides
Let's calculate the lengths of the sides using the distance formula:

Side AB:
AB = √[(x2 - x1)^2 + (y2 - y1)^2]
AB = √[(4 - (-4))^2 + (0 - 0)^2]
AB = √[8^2 + 0^2]
AB = √64
AB = 8

Side BC:
BC = √[(x2 - x1)^2 + (y2 - y1)^2]
BC = √[(0 - 4)^2 + (3 - 0)^2]
BC = √[(-4)^2 + 3^2]
BC = √[16 + 9]
BC = √25
BC = 5

Side AC:
AC = √[(x2 - x1)^2 + (y2 - y1)^2]
AC = √[(-4 - 0)^2 + (0 - 3)^2]
AC = √[(-4)^2 + (-3)^2]
AC = √[16 + 9]
AC = √25
AC = 5

Explanation
In this case, we find that side AB has a length of 8 units, while sides BC and AC both have a length of 5 units.

Conclusion
Since two sides of the triangle have the same length (5 units), this triangle is classified as an isosceles triangle.

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