Question

a triangle has verticles a (0,-5), b (-2,1)and c (10,5) show that is right angled triagnle

Answer 1

Answer:

Since two lines are perpendicular to each other, it is a right-angled triangle.

Step-by-step explanation:

If this is a right angled triangle, two lines joining any two of these points must be at 90° to each other.

In such condition, if m₁ and m₂ are the slopes of those two lines, then

                    m₁m₂ = -1

Slope of line joining A(0, -5) and B(-2, 1):

   ⇒ (y₂ - y₁)/(x₂ - x₁)

   ⇒ (1 - (-5)) / (-2 - 0)

   ⇒ -3              ...(1)

Slope of line joining A(0, -5) and C(10 , 5):

   ⇒ (-5 - 5)/(0 - 10)

   ⇒ 1               ...(2)

Slope of line joining B(-2, 1) and C(10 , 5)

   ⇒ (1 - 5)/(-2 - 10)

   ⇒ 4/12

   ⇒ 1/3            ...(3)

Notice that (1) * (3) = -1    [-3 * 1/3 = -1]

 Hence, there is a right angle, this means it is a right-angled triangle.

Answer 2

for further explanation please refer the above attachment