Question P(x, y), A (5, 1) and B (–1, 5) are the given points. If the distance of P (x, y) from A (5, 1) and B(–1, 5) are equal, prove that 3x = 2y. Let A and B denote the points (5, 4) and (–2, 3), respectively. Therefore, coordinates of the point P are (x, 0). Question Since the required point (say P) is on the X-axis, its ordinate will be zero.
Find a point on the X-axis which is equidistant from the points (5, 4) and (-2, 3). Since, AB + BC =, the points A, B and C are collinear. Points A, B and C will be collinear, if the sum of the lengths of two line-segments is equal to the third. Question Let the given points (-3, 2), (1, -2) and (9, -10) be denoted by A, B and C, respectively. Using distance formula, show that the points (-3, 2), (1, -2) and (9, -10) are collinear. Question Let the point and (1, 2) be denoted by P, Q and R, respectively. Prove that the points and (1, 2) are the vertices of an isosceles triangle. Question Let A(1, – 1), B(5, 2) and (9, 5) be the given points. Show that the points (1, –1), (5, 2) and (9, 5) are collinear. 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. For example, 15-06-22, 15.06.22 and 15:06:22 are all interpreted as 15 hours 6 minutes 22 seconds or 15:06:22.In particular, the distance of a point P(x, y) from the origin O(0, 0) is given by OP = √x 2 + y 2.
You can use a dash (-), period (.) or colon (:) as separators and must always use 2 separators. Time = distance/speed Time Entry Formats hh:mm:ss To solve for time use the formula for time, t = d/s which means time equals distance divided by speed. To solve for speed or rate use the formula for speed, s = d/t which means speed equals distance divided by time. You can use the equivalent formula d = rt which means distance equals rate times time. Rate and speed are similar since they both represent some distance per unit time like miles per hour or kilometers per hour. To solve for distance use the formula for distance d = st, or distance equals speed times time. Time can be entered or solved for in units of secondes (s), minutes (min), hours (hr), or hours and minutes and seconds (hh:mm:ss). The Speed Distance Time Calculator can solve for the unknown Calculate speed, distance or time using the formula d = st, distance equals speed times time.
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