Q. 103.9( 17 Votes )

# Let us write by calculation whether the three points O (0, 0), A(4, 3) and B(8, 6) are collinear.

Answer :

We have O → (0, 0)

A → (4, 3)

B → (8, 6)

The distance of a point (x,y) from origin is given as , so

OA

= 5

and OB

= 10

We know that distance between two points (x_{1}, y_{1}) and (x_{2}, y_{2}) is given by .

Using the above distance formula,

AB

= 5

We find that,

OA + AB = 5 + 5 = 10 = OB

⇒ The points A, B and C are collinear.

Rate this question :

The triangle formed by the points (3, 0), (–3, 0) and (0, 3) is

West Bengal MathematicsLet us calculate the distances of the following points from origin:

(i) (7, –24)

(ii) (3, –4)

(iii) (a + b, a – b)

West Bengal MathematicsLet us calculate the distances between the two points given below:

(i) (5, 7) and (8, 3)

(ii) (7, 0) and (2, –12)

(iii) and (0, –2)

(iv) (3, 6) and (–2, –6)

(v) (1, –3) and (8, 3)

(vi) (5, 7) and (8, 3)

West Bengal MathematicsLet us prove that the point (–2, –11) is equidistant from the two points (–3, 7) and (4, 6).

West Bengal MathematicsIf the distance of the point (x, 4) from the origin is 5 units, then the values of x are

West Bengal MathematicsLet us show that the three points (2, 2), (–2, –2) and are the vertices of an equilateral triangle.

West Bengal MathematicsLet us prove that the three points A(3, 3), B(8, –2) and C(–2, –2) are the vertices of a right-angled isosceles triangle. Let us calculate the length of the hypotenuse of ΔABC.

West Bengal MathematicsLet us calculate and see that for what value of y, the distance of the two points (2, y) and (10, –9) will be 10.

West Bengal MathematicsLet us find a point on x-axis which is equidistant from the two points (3, 5) and (1, 3).

West Bengal Mathematics