![]() Find the distance between the points P(–6, 7) and Q(–1, –5). Then, by distance formula, we obtain the distance PQ as Question Let the points (8, -2) and (3, -6) be denoted by P and Q, respectively. Find the distance between the points (8, -2) and (3, -6). ![]() For three points to be collinear - We have to prove that the sum of the distances between two pairs of points is equal to the third pair of points. (vii) For a Parallelogram - We have to prove that the opposite sides are equal (and there is no need to establish that two diagonals are unequal the rectangle is also a parallelogram).Ģ. ![]() (vi) For a rectangle - We have to prove that the opposite sides are equal and two diagonals are equal. (v) For a rhombus - We have to prove that four sides are equal (and there is no need to establish that two diagonals are unequal as the square is also a rhombus). (iv) For a square - We have to prove that the four sides are equal, two diagonals are equal. (iii) For a right -angled triangle - We have to prove that the sum of the squares of two sides is equal to the square of the third side. (ii) For an equilateral triangle - We have to prove that three sides are equal. (i) For an isosceles triangle - We have to prove that at least two sides are equal. In questions relating to geometrical figures, take the given vertices in the given order and proceed as indicated. ![]() In particular, the distance of a point P(x, y) from the origin O(0, 0) is given by OP = √x 2 + y 2. ![]()
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