Question

using the slope concept, show that the points (1,-4),(2,-3), and (4,-7) form a right angled triangle

Answer 1

Proof:

Let the given points are P (1, - 4), Q (2, - 3) and R (4, - 7).

Then the slope of the line PQ is

= (- 3 + 4) / (2 - 1) = 1 / 1 = 1,

the slope of the line QR is

= (- 7 + 3) / (4 - 2) = - 4 / 2 = - 2

and the slope of the line RP is

= (- 4 + 7) / (1 - 4) = 3 / (- 3) = - 1

Here the slope of the line PQ × the slope of the lime RP is

= 1 × (- 1) = - 1

We can conclude that the two lines PQ and RP are perpendicular to each other. Then ∠P = 90°

Therefore if the points P, Q, R make a triangle, the angle ∠P being a right angle, ΔPQR is a right-angled triangle.

Hence proved.

Answer 2

Answer:

Step-by-step explanation:

Proof:

Let the given points are P (1, - 4), Q (2, - 3) and R (4, - 7).

Then the slope of the line PQ is

= (- 3 + 4) / (2 - 1) = 1 / 1 = 1,

the slope of the line QR is

= (- 7 + 3) / (4 - 2) = - 4 / 2 = - 2

and the slope of the line RP is

= (- 4 + 7) / (1 - 4) = 3 / (- 3) = - 1

Here the slope of the line PQ × the slope of the lime RP is

= 1 × (- 1) = - 1

We can conclude that the two lines PQ and RP are perpendicular to each other. Then ∠P = 90°

Therefore if the points P, Q, R make a triangle, the angle ∠P being a right angle, ΔPQR is a right-angled triangle.

Hence proved.