Victory for the ACT Student Text 15e

L ESSON 3 | C OORDINATE G EOMETRY • 231

DISTANCE AND MIDPOINT FORMULAS

Šƒ– ‹• –Š‡ †‹•–ƒ…‡ „‡–™‡‡ –Š‡ ’‘‹–• ( , ) 3 2 and ( , )3 3 ? F. 3 G. 2 3

 –Š‡ ϐ‹‰—”‡ „‡Ž‘™ǡ ™Šƒ– ‹• –Š‡ ƒ”‡ƒ ‘ˆ –Š‡ square region?

16.

18.

Throwback to Math Class The distance formula is derived from the Pythagorean theorem for a right triangle, in ™Š‹…Š –Š‡ †‹•–ƒ…‡ length corresponds to the hypotenuse: d . x x y y 2 1 2 2 1 2 − + − ^ ^ h h Throwback to Math Class The midpoint „‡–™‡‡ ƒ ’‘‹– ™‹–Š coordinates ( , ) x y 1 1 ƒ† ƒ ’‘‹– ™‹–Š coordinates ( , ) x y 2 2 has coordinates , x x y y 2 2 1 2 1 2 c m .

H. 5 J. 29 K. 61

 –Š‡…‘‘”†‹ƒ–‡ ’Žƒ‡ „‡Ž‘™ǡ MO MN , and MO MN = . What is the value of y ?

17.

F. 4 G. 8 H. 8 2 J. 16 K. 25

 –Š‡…‘‘”†‹ƒ–‡ ’Žƒ‡ǡ ™Šƒ– ‹• –Š‡ ‹†’‘‹– ‘ˆ –Š‡ Ž‹‡ •‡‰‡– ™‹–Š endpoints (–3,–5) and (5,7)? A. (1,1) B. (1,6) C. 3, 2 7 c m D. (4,6) E. (8,12)

19.

A. 5 B. 7 C. 12 D. 13 E. 17