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So, the graph of the given points is

P Pankaj Sanodiya
Let the points (1, 5), (2, 3), and (- 2,-11) be representing the vertices A, B, and C of the given triangle respectively. Let A = (1, 5), B = (2, 3) and C = (- 2,-11) So The distance AB : The distance BC : The distance CA : As we can see that   AB + BC ≠ CA Therefore, the points (1, 5), (2, 3), and ( - 2, - 11) are not collinear.

D Divya Prakash Singh
From the figure: (i) The coordinates of B are  (ii) The coordinates of C are  (iii) The point is E identified by the coordinates (–3, –5). (iv) The point is G identified by the coordinates (2, – 4). (v) The abscissa of the point D is 6. (vi) The ordinate of the point H is -3. (vii) The coordinates of the point L are  (viii) The coordinates of the point M are

D Divya Prakash Singh
The point where x-axis and y-axis both intersect is known as Origin.

D Divya Prakash Singh
The name of each part of the plane formed by the x-axis and the y-axis is called "Quadrant".

D Divya Prakash Singh
The Horizontal line is x-axis and the Vertical line is y-axis.

D Divya Prakash Singh
(ii) From the figure: The cross street as shown by the point  We have located the two cross streets because of the two reference lines.

D Divya Prakash Singh
(i) From the figure: There is only one cross - streets which can be referred to as (4, 3).

D Divya Prakash Singh
To describe the position of a table lamp placed on the table, Let us consider the table lamp as P and the table as a plane. Then, we consider two perpendicular edges of the table as the axes OX and OY. From OY measure the perpendicular distance  of P. From OX measure the perpendicular distance  of P. Thus, the position of the lamp is then given by;

D Divya Prakash Singh
From the figure: P is the mid-point of side AB. Therefore, the coordinates of P are,  Similarly, the coordinates of Q, R and S are: respectively. The distance between the points P and Q: and the distance between the points Q and R: Distance between points R and S: Distance between points S and P: Distance between points P and R the diagonal length: Distance between points Q and S the...

D Divya Prakash Singh
From the figure, Let the median be AD which divides the side BC into two equal parts. Therefore, D is the mid-point of side BC. Coordinates of D: Let the centroid of this triangle be O. Then, point O divides the side AD in a ratio 2:1. Coordinates of O:

D Divya Prakash Singh
We observed that the coordinates of P, Q, and R are the same. Therefore, all these are representing the same point on the plane. i.e., the centroid of the triangle.

D Divya Prakash Singh
From the figure,  The point Q divides the median BE in the ratio, BQ : QE = 2 : 1 Hence using the section formula, The point R divides the median CF in the ratio, CR : RF = 2 : 1 Hence using the section formula,

D Divya Prakash Singh
From the figure, The point P divides the median AD in the ratio, AP : PD = 2 : 1 Hence using the section formula,

D Divya Prakash Singh
From the figure: Let AD be the median of the triangle Then, D is the mid-point of BC Coordinates of Point D:

D Divya Prakash Singh
From the figure: Given ratio: Therefore, D and E are two points on side AB and AC respectively, such that they divide side AB an AC in the ratio of . Section formula: Then, coordinates of point D: Coordinates of point E: Then, the area of a triangle: Substituting the values in the above equation, Hence the ratio between the areas of  and  is

D Divya Prakash Singh
Taking C as origin, then CB will be x-axis and CD be y-axis. The coordinates fo the vertices P,Q, and R are:  respectively. The area of the triangle, in this case, will be: It can be observed that in both cases the area is the same so, it means that the area of any figure does not depend on the reference which you have taken.