Find the distance between the points 0, 0 and 36, 15. Can you now find the distance between the two towns A and B discussed in Section 7. Answer Distance between points 0, 0 and 36, 15 Yes, Assume town A at origin point 0, 0. Therefore, town B will be at point 36, 15 with respect to town A. And hence, as calculated above, the distance between town A and B will be 39 km. Determine if the points 1, 52, 3 and -2, -11 are collinear. Answer Let the points 1, 52, 3and - 2,-11 be representing the vertices A, B, and C of the given triangle respectively. Check whether 5, — 26, 4 and 7, — 2 are the vertices of an isosceles triangle. Answer Let the points 5, — 26, 4and ncert solution for class 12 maths chapter 7, — 2 are representing the vertices A, B, and C of the given triangle respectively. In a classroom, 4 friends are seated at the points A, B, C and D as shown in the following figure. Using distance formula, find which of them is correct. Answer Clearly from the figure, the coordinates of points A, B, C and D are 3, 46, 79, 4 and 6, 1. Name the type of quadrilateral formed, if any, by the following points, and give reasons for your answer: i - 1, — 21, 0- 1, 2- 3, 0 ii - 3, 53, 10, 3- 1, — 4 iii 4, 57, 64, 31, 2 Answer Let the points — 1, — 21, 0— 1, 2and — 3, 0 be representing the vertices A, B, C, and D of the given quadrilateral respectively. It can be observed that all sides of this quadrilateral are of the same length and also, the diagonals are of the same length. Therefore, the given points are the vertices of a square. It can be observed that all sides of this quadrilateral are of different lengths. Therefore, it can be said that it is only a general quadrilateral, and not specific such as square, rectangle, etc. It can be observed that opposite sides of this quadrilateral are of the same length. However, the diagonals are of different lengths. Therefore, the given points are the vertices of a parallelogram. Find the point on the x-axis which is equidistant from 2, — 5 and - 2, 9. Answer We have to find a point on x-axis. Therefore, its y-coordinate will be 0. Find the values of y for which the distance between the points P 2, — 3 and Q 10, y is 10 ncert solution for class 12 maths chapter 7. Answer It is given that the distance between 2, — 3 and 10, y is 10. If Q 0, 1 is equidistant from P 5, — 3 and R x, 6find the values of x. When point R is 4, 610. Find a relation between x and y such that the point x, y is equidistant from the point 3, 6 and - 3, 4. Answer Point x, y is equidistant from 3, 6 and — 3, 4. Find the coordinates of the point which divides the join of - 1, 7 and 4, — 3 in the ratio 2:3. Answer Let P x, y be the required point. Using the section formula, we get Therefore, the point is 1, 3. Find the coordinates of the points of trisection of the line segment joining 4, -1 and -2, -3. Answer Let P x 1, y 1 and Q x 2, y 2 are the points of trisection of the line segment joining the given points i. What is the distance between both the flags. If Rashmi has to post a blue flagexactly halfway between the line segment joining the two flags, where should she post her flag. Therefore, the coordinates of this point G is 2, 25. Therefore, the coordinates of this point R are 8, 20. Find the ratio in which the line segment joining the points -3, 10 and 6, — 8 is divided by -1, 6. Answer Let the ratio in which the line segment joining -3, 10 and 6, -8 is divided by point -1, 6 be k : 1. Find the ratio in which the line segment joining A 1, — 5 and B - 4, 5 is divided by the x-axis. Also find the coordinates of the point of division. Answer Let the ratio in which the line segment joining A 1, — 5 and B — 4, 5 is divided by x-axisbe. We know that y-coordinate of any point on x-axis is 0. If 1, 24, yx, 6 and 3, 5 are the vertices of a parallelogram taken in order, find x and y. Answer Let A,B,C and D be the points 1,2 4, yx,6 and 3,5 respectively. Answer Let the coordinates of point A be x, y. Answer The coordinates of point A and B are -2,-2 and 2,-4 respectively. Find the coordinates of the points which divide the line segment joining A - 2, 2 and B 2, 8 into four equal parts. Answer From the figure, it can be observed that points X, Y, Z are dividing the line segment in a ratio 1:3, 1:1, 3:1 respectively. Find the area of a rhombus if its vertices are 3, 04, 5-1, 4 and -2,-1 taken in order. Page No: 170 Exercises 7. Find the area of the triangle formed by joining the mid-points of the sides of the triangle whose vertices are 0, -12, 1 and 0, 3. Find the ratio of this area to the area of the given triangle. Answer Let the vertices of the triangle be A 0, -1B 2, 1C 0, 3. Let D, E, F be the mid-points of the sides of this triangle. Find the area of the quadrilateral whose vertices, taken in order, are -4, -2-3, -53, -2 and 2, 3. Answer Let the vertices of the quadrilateral be A — 4, — 2B — 3, — 5C 3, — 2and D 2, 3. Answer Let the vertices of the triangle be A 4, -6B 3, -2and C 5, 2. The area of both sides is same.
