The points A(0, 6), B(-5, 3) and C(3, 1) are the vertices of a triangle which is ?a)equilateralb)right angledc)isoscelesd)scaleneCorrect answer is option 'C'. Can you explain this answer?

Question

Answer

First Form a triangle using given vertices.
Then calculate distance for all the sides .
Then you will get two sides of equal distances.
So it is an isosceles triangle.

Answer

We can see,AB^2   AC^2 =34   34 = 68 = BC^2So it is isosceles right angled triangle.

Answer

C

Answer

AB²= (-5 - 0)² + (-3 - 0)² = 25 + 9 = 34

BC² = (3 + 5)² + (1-3)² = 8² + (-2)² = 64 + 4 = 68

AC² = (3 - 0)² + (1 - 6)² = 9 + 25 = 34.

AB = AC. ==> ΔABC is isosceles.

Answer

Solution:

In order to determine the type of triangle, we need to find the length of all three sides of the triangle using the distance formula.

Distance Formula: The distance between two points (x1, y1) and (x2, y2) is given by

d = √((x2-x1)² + (y2-y1)²)

Using the distance formula, we get:

AB = √((3-0)² + (-3)²) = √(9+9) = √18

BC = √((3-(-5))² + (1-3)²) = √64 = 8

AC = √((3-0)² + (1-6)²) = √50

Therefore, AB ≠ BC ≠ AC, which means that the triangle is not equilateral or isosceles.

Now, let us find the slopes of the sides of the triangle.

Slope Formula: The slope of a line passing through two points (x1, y1) and (x2, y2) is given by

m = (y2-y1)/(x2-x1)

Using the slope formula, we get:

Slope of AB = (3-6)/(-5-0) = 3/5

Slope of BC = (1-3)/(3-(-5)) = -1/4

Slope of AC = (1-6)/(3-0) = -5/3

Since the product of the slopes of AC and BC is -1 (i.e., (mAC x mBC) = (-5/3 x -1/4) = 5/12 ≠ -1), the triangle is not right angled.

Therefore, the triangle is scalene, i.e., all three sides are of different lengths and no two angles are equal.

Answer

AB²= (-5 - 0)² + (-3 - 0)² = 25 + 9 = 34

BC² = (3 + 5)² + (1-3)² = 8² + (-2)² = 64 + 4 = 68

AC² = (3 - 0)² + (1 - 6)² = 9 + 25 = 34.

AB = AC. ==> ΔABC is isosceles.

Answer

AB²= (-5 - 0)² + (-3 - 0)² = 25 + 9 = 34

BC² = (3 + 5)² + (1-3)² = 8² + (-2)² = 64 + 4 = 68

AC² = (3 - 0)² + (1 - 6)² = 9 + 25 = 34.

AB = AC. ==> ΔABC is isosceles.

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