Question

Bart is jogging on a circular trail in a state park. The diameter of the trail is 650 meters. What approximate distance does Bart cover in one lap around the park?
1,326,650 meters
331,662.5 meters
2,041 meters
1,020.5 meters

Answer 1

Step-by-step explanation:

(i) Since the line joining A(2,3) and B(6,-5) meets the x-axis at P, then the y-coordinate of P is zero(0).

(ii) Let the coordinate of point P is (x,0), also the point P lies between A and B.

Let the ratio of AP:PB be k:1

By section formula,

x=

m

1

+m

2

m

1

x

2

+m

2

x

1

⇒x=

k+1

1.6+k.2

=

k+1

6+2k

and,y=

m

1

+m

2

m

1

y

2

+m

2

y

1

⇒0=

k+1

k.(−5)+1.3

⇒k=

5

3

therefore ratio of AP:PB=3:5

(iii) since P(2,3) is the midpoint of A(x',0) and B(0,y') (from the figure)

∴x=

2

x

1

+x

2

⇒x

′

=4

and,y=

2

y

1

+y

2

⇒y

′

=6

therefore coordinate of A and B is (4,0) and (0,6) respectively.