Question

CASE STUDY QUESTION Three friends : R, L and S go to the same school and live in the same neighbour-hood, but they are at different locations in the playground. They are connected by a path of distances which varies for each one of them differently as showning the respective image below.

6. Using distance formula, find distance between R and S.
1 point
(a) 7.36 units
(b) 5.21 units
(c) 6.52 units
(d) 8.23 units
7. Find the point which is equidistant from R and L.
1 point
(a) (1,0)
(b) (0,1)
(c) (0,0)
(d) none of these
8. Locate the coordinate of L.
1 point
(a) (-1,2)
(b) (0,-2)
(c) (0,3)
(d) none of these
9. Find the coordinates of the point which divides the line segment of L and S in 1:1.
1 point
(a) (3,2)
(b) (2,3)
(c) (-3,2)
(d) (3,-2)
10. What is the mid point of RS?
1 point
(a) (0,0)
(b) (3,0)
(c) (0, 3)
(d) (3,1)​

Answer 1

6.

Distance Formula : \sqrt{(x2-x1)^{2}+(y2-y1)^{2}  }

= \sqrt{(6-0)^{2}+(-2-2)^{2}  }

= \sqrt{(6)^{2}+(-4)^{2}  }

= \sqrt{12+16}

= \sqrt{28}

= 5.291

(b) 5.21 units

7.

(c) (0,0)

8.

(b) (0,-2)

9.

Required Co-ordinates of the point= (\frac{mx2+nx1}{m+n} ,\frac{my2+ny1}{m+n} )

Here, m=1 and n=1 , x1=6, y1=-2, x2=0, y2=-2

therefore, Required Points =  (\frac{(1)(0)+(1)(6)}{1+1} ,\frac{(1)(-2)+(1)(-2)}{1+1} )

=  (\frac{6}{2} ,\frac{-4}{2} )

=(3,-2)

(d) (3,-2)

10.

Mid-Point Formula, (x_{m},y_{m}  ) = (\frac{x1+x2}{2} ,\frac{y1+y2}{2} )

(x_{m},y_{m})= (\frac{0+6}{2} ,\frac{2+(-2)}{2} )

(x_{m},y_{m})= (\frac{6}{2} ,\frac{0}{2} )

(x_{m},y_{m})= (3,0)

(b) (3,0)

Answer 2

Step-by-step explanation:

the step by step solution is provided in the uploaded snap . kindly find the attachment