Question

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?

• A. $(7,5)$
• B. $(5,7)$
• C. $(4,6)$
• D. $(6,4)$

Answer 1

Answer: (A)

$GiventhatABCDisasquarewithA(x_1,y_1)=(3,5),B(x_2,y_2)=(7,8)C(x_3,y_3)=(11,5)andD(x_4,y_4)=(7,2).\therefore ThepositionofJaspalwillbethemidpointM(x,y)betweenACorBD.(AC=BD\because ABCDisasquare).BythesectionformulaforthemidpointM(x,y)=(\frac{x_1+x_3}{2},\frac{y_1+y_3}{2})orM(x,y)=(\frac{x_2+x_4}{2},\frac{y_2+y_4}{2}).⟹M(x,y)=(\frac{3+11}{2},\frac{5+5}{2})orM(x,y)=(\frac{7+7}{2},\frac{8+2}{2})⟹M(x,y)=(7,5).Sotheposition(co-ordinates)ofJaspalis(7,5).Ans-Theposition(co-ordinates)ofJaspalis(7,5).$