A city has streets that run north and south and avenues that run east and west, all equally spaced. Streets and avenues are numbered sequentially, as shown in the figure.

Question

A city has streets that run north and south and avenues that run east and west, all equally spaced. Streets and avenues are numbered sequentially, as shown in the figure. The walking distance between points A and B is 7 blocks—that is, 3 blocks east and 4 blocks north. To find the straight-line distance d, we must use the Distance Formula.

(a) Find the straight-line distance (in blocks) between A and B.

(b) Find the walking distance and the straight-line distance between the corner of 2nd St. and 2nd Ave. and the corner of 12th St. and 26th Ave.

(c) What must be true about the points P and Q if the walking distance between P and Q equals the straight-line distance between P and Q?

Points P and Q must be on the same street and the same avenue.

Points P and Q must either be on the same street or the same avenue.

Points P and Q must be on different streets and different avenues.

Points P and Q must either be on different streets or different avenues.

There is not enough information.

Answer 1

a) distance between A and B = d= sqr(16+9) = sqr25 = 5