Q. 64.1( 14 Votes )

# Find the distance between the following points:

(i) (–6, 7) and (–1, –5)

(ii) (–1, –1) and (8, –2)

(iii) (at_{1}^{2}, 2at_{1}) and (at_{2}^{2}, 2at_{2})

Answer :

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

(i) Let the points (–6, 7) and (–1, –5) be A and B respectively, so the distance between them

(ii) Let the points (–1, –1) and (8, –2) be A and B respectively, so the distance between them

(iii) Let the points (at_{1}^{2}, 2at_{1}) and (at_{2}^{2}, 2at_{2}) be A and B respectively, so the distance between them

Rate this question :

If the coordinates of P and Q are (a cos θ, b sin θ) and (–a sin θ, b cos θ) respectively, then prove that OP^{2} + OQ^{2} = a^{2} + b^{2}, where O is the origin.

Prove that the mid–point C of the hypotenuse in a right angled triangle AOB is situated at equal distances from the vertices O, A and B of the triangle.

Rajasthan Board MathematicsIf two vertices of an equilateral triangle are (0, 0) and then find the third vertex.

Rajasthan Board MathematicsThe distance of point (3, 4) from y-axis will be:

Rajasthan Board MathematicsThe distance between the points (0, 3) and (–2, 0) will be:

Rajasthan Board MathematicsThe distance of point (5, –2) from x-axis will be:

Rajasthan Board MathematicsThe quadrilateral formed by points (–1, 1), (0, –3), (5, 2) and (4, 6) will be:

Rajasthan Board MathematicsThe opposite vertices of a square are (5, –4) and (–3, 2) find the length of its diagonal.

Rajasthan Board MathematicsIf the vertices of a quadrilateral are (1, 4), (–5, 4), (–5, –3) and (1, –3), then find the type of quadrilateral.

Rajasthan Board MathematicsIf the distances of the point (0, 2) from the points (3, k) and (k, 5) are equal then find the value of k.

Rajasthan Board Mathematics