18. SPORTS DAYIn a sports day celebration ,the school decided to make activity between students in such a way that Vicky ,Garvit ,and Shalini are standing at positions A, B ,and C whose coordinates are (3,3) ,(5,9) and (9,3) respectively. The teacher asked Deepanshi to fix the country flag at the midpoint of the line joining point A and B.
(i) Find the coordinates of midpoint of A and B.
a. (4, 6) b. (3, 4) c. (4, 4) d. (3,3 )
(ii) Find the distance between Garvit and Vicky .
3 √10 (b) 2 √ 10 (c)√ 10 (d) ) 4 √ 10
(iii) Find the distance between Vicky and Shalini.
6 (b) 8 (c) 9 (d) 74
(iv) Find the point on x axis , which is equidistant from points A and C
(a) (0,-6) (b) (6,0) (c) (5,3) (d) (9,5)
(v) If the vertices of a ∆PQR are (x1,y1) , (X2, Y2) and(X3, Y3), then centroid of a ∆PQR is
(a) (x1+x2+x3 /2 , y1+y2+y3/2)
(b) (x1+x2+x3/3, y1+y2+y3/3)
(c) (x1+x2/2)
Answers
Answer:
(i) the answer is (a) (4, 6)
(ii) the answer is (b) 2 √ 10
(iii) the answer is (a) 6
(iv) the answer is (b) (6,0)
(v) the answer is (b) (x1+x2+x3/3, y1+y2+y3/3)
Step-by-step explanation:
(i) The coordinates of the midpoint of a line can be found by taking the average of the x-coordinates and the y-coordinates of the two endpoints. So, the midpoint of A and B would be:
((3 + 5) / 2, (3 + 9) / 2) = (4, 6)
So the answer is (a) (4, 6)
(ii) The distance between two points can be found using the distance formula:
√((x2-x1)^2 + (y2-y1)^2)
The coordinates of point A and B are (3,3) and (5,9) respectively
so the distance between point A and B = √((5-3)^2 + (9-3)^2) = √10
So the answer is (b) 2 √ 10
(iii) The coordinates of point Vicky and Shalini are (3,3) and (9,3) respectively.
so the distance between point Vicky and Shalini = √((9-3)^2 + (3-3)^2) = 6
So the answer is (a) 6
(iv) A point on the x-axis will have a y-coordinate of 0. To find the point that is equidistant from A and C, we can use the midpoint formula again:
((x1 + x2) / 2, (y1 + y2) / 2) = (6, 0)
So the answer is (b) (6,0)
(v) The centroid of a triangle is the point where the medians of the triangle intersect. The median of a triangle is the line segment from a vertex to the midpoint of the opposite side. The centroid is the point where the medians of the triangle intersect, which is the average of the x-coordinates and the y-coordinates of the three vertices. So the centroid of a triangle PQR with vertices (x1,y1), (x2,y2), and (x3,y3) would be:
(x1+x2+x3 /3, y1+y2+y3/3)
So the answer is (b) (x1+x2+x3/3, y1+y2+y3/3)
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Answer:
(b) (x1+x2+x3/3, y1+y2+y3/3)
Step-by-step explanation:
I, the response is (a) (4, 6)
The response to (ii) is (b) 2 10.
The response to (iii) is (a) 6.
(iv) The response is (b) (6,0)
The correct response is (b) (x1+x2+x3/3, y1+y2+y3/3).
Detailed explanation:
I By averaging the x- and y-coordinates of the two endpoints, it is possible to determine the coordinates of a line's midway. So, A and B's halfway point would be:
((3 + 5) / 2, (3 + 9) / 2) = (4, 6) (4, 6)
The response is (a) (4, 6)
(ii) The distance formula can be used to calculate the separation between two points
√((x2-x1)^2 + (y2-y1)^2)
Points A and B are located at coordinates (3,3) and (5,9), respectively.
As a result, the distance between points A and B is equal to (10 + (5-3) + (9-3)).
So the response is (b) 2 10.
(iii) Vicky and Shalini's respective locations are (3,3) and (9,3).
Therefore, the distance between Vicky and Shalini is equal to 6 (((9-3)2 + (3-3)2).
the response is (a) 6
(iv) The y-coordinate of a point on the x-axis will always be 0. We may apply the midpoint formula once more to determine the location that is equally distant from A and C:
((x1 + x2) / 2, (y1 + y2) / 2) = (6, 0) (6, 0)
The response is (b) (6,0)
The intersection of a triangle's medians is where the triangle's centroid is located (v). The line segment connecting a triangle's vertex to the middle of the other side is known as the median. The triangle's centroid is the location where its medians meet.
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