Question

The points (1,1), (-2, 7) and (3, -3) are


1.vertices of an equilateral triangle


2.collinear


3.vertices of an isosceles triangle


4.none of these

Answer 1

Explanation:-

These points (1,1), (-2,7) and (3,-3) forms collinear.

you can actually see in the Attachment the given points have been plotted forms a straight segment or line.

here it is collinear because the segBC is equals to seg AB + segAC.

That means d(BC) = d(BA) + d(AC)

by using distance formula we can show that these points are collinear.

A = (1,1) = (x1, y1)

B = (-2,7) = (x2,y2)

C = (3,-3) = (x3,y3)

d(BC) = d(BA) + d(AC)

By distance formula

√((x3 - x2)² + (y3 - y2)²) = √((x2 - x1)² + (y2 - y1)²) + √((x3 - x1)² + (y3 - x1)²)

√((3-(-2))² + (-3-7)²) = √((-2-1)² + (7-1)²) + √((3-1)² + (-3-1)²)

√((5)² + (-10)²) = √((-3)² + (6)² ) + √((2)² + (-4)²)

√(25 + 100) = √(9 + 36) + √(4 + 16)

√(125) = √(45) + √(20)

5√(5) = 3√(5) + 2√(5)

5√(5) = 3√(5) + 2√(5)5√(5) = 5√(5)

In this way they are collinear.

option 2. collinear

Answer 2

Answer:

Option 2: Collinear

☺️☺️☺️☺️☺️☺️☺️☺️☺️☺️☺️☺️