Students of a school are standing in rows and columns in their playground for a drill practice. A, B, C and D are the positions of four students as shown in figure 7.4. Is it possible to place Jaspal in the drill in such a way that he is equidistant from each of the four students A, B, C and D? If so, what should be his position?
Solution:
Given, school students are standing in rows and columns in their playground for a drill practice.
The position of four students A, B, C and D are shown in the figure 7.4
We have to find the position of Jaspal in the drill in such a way that he is equidistant from each of the four students.
From the figure,
The position of student A = (3, 5)
The position of student B = (7, 9)
The position of student C = (11, 5)
The position of student D = (7, 1)
We observe from the figure that the position of students ABCD is a square.
Since Jaspal has to be positioned in such a way that he is equidistant from all the four students,
The position of Jaspal will be the midpoint between AC or BD.
The coordinates of the mid-point of the line segment joining the points P (x₁ , y₁) and Q (x₂ , y₂) are [(x₁ + x₂)/2, (y₁ + y₂)/2]
Midpoint of A(3, 5) and C(11, 5) = [(3 + 11)/2, (5 + 5)/2]
= [14/2, 10/2]
Midpoint of AC = [7, 5]
Midpoint of B(7, 9) and D(7, 1) = [(7 + 7)/2, (9 + 1)/2]
= [14/2, 10/2]
Midpoint of BD = [7, 5]
Therefore, the position of Jaspal is the midpoint of AC or midpoint of BD = [7, 5]
✦ Try This: On the playground, if the children are made to stand for drill either 20 to a row or 25 to a row, all rows are complete and no child is left out. What is the lowest possible number of children in that school?
☛ Also Check: NCERT Solutions for Class 10 Maths Chapter 7
NCERT Exemplar Class 10 Maths Exercise 7.4 Problem 5
Students of a school are standing in rows and columns in their playground for a drill practice. A, B, C and D are the positions of four students as shown in figure 7.4. Is it possible to place Jaspal in the drill in such a way that he is equidistant from each of the four students A, B, C and D? If so, what should be his position
Summary:
Students of a school are standing in rows and columns in their playground for a drill practice. A, B, C and D are the positions of four students as shown in figure 7.4. It is possible to place Jaspal in the drill in such a way that he is equidistant from each of the four students A, B, C and D. His position is the midpoint of AC or midpoint of BD = (7, 5)
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