AccelePrep for the ACT Test 2nd Edition Student Text

C HAPTER 4 | F AST T RACK TO M ATH M ECHANICS • 93

‹…‡ ‹–ǯ• ƒ Ͷͷ q -45 q -90 q triangle, the x - and y Ǧ…‘‘”†‹ƒ–‡• ƒ”‡ ‡“—ƒŽǤ •‡ –Š‡ ›–Šƒ‰‘”‡ƒ –Š‡‘”‡ –‘ •‘Ž˜‡ ˆ‘” x and y : s s s s 2 4 2 2 2 2 2 2 & & Ǥ Š‡ coordinates of A are ( , ) 2 2 Ǥ ȋ ‘—…ƒ ƒŽ•‘ •‘Ž˜‡ ˆ‘” –Š‡ sides of the isosceles triangle using –Š‡ ”ƒ–‹‘ ‘ˆ –Š‡ •‹†‡• ƒ• ‰‹˜‡ ‹ –Š‡ ”‡ˆ‡”‡…‡ section of the directions, but this method is Ž‘‰‡”ǤȌ Check your answer Ǥ Š‡ “—‡•–‹‘ ƒ•‡† ˆ‘” –Š‡ coordinates of A , ( , ) 2 2 ǡ •‘ –Š‡ ƒ•™‡” ‹• ȋ ȌǤ

10. (H) Mathematics/Geometry/Circles and Algebra and Functions/Coordinate Geometry/The Coordinate System Preview the question. Š‹• ‹• ƒ †‹ˆϐ‹…—Ž– ‹–‡Ȅ †‘ǯ– Ž‘‘ ˆ‘” ‡ƒ•› ƒ•™‡”•Ǥ ϐ‹‰—”‡ ‹• ‘– ‹…Ž—†‡†ǡ •‘ ›‘— •Š‘—Ž† †”ƒ™ ‘‡Ǥ Š‡ “—‡•–‹‘ asks for the coordinates of point A ǡ ™Š‹…Š Šƒ˜‡ –‘ „‡ †‡”‹˜ƒ„Ž‡ ˆ”‘ –Š‡ ‰‹˜‡ ‹ˆ‘”ƒ–‹‘ •‹…‡ ƒ…ƒŽ…—Žƒ–‘” ‹• ‘– ƒŽŽ‘™‡†Ǥ Strategize and solve Ǥ ”ƒ™ ƒ ’‹…–—”‡ ‘ˆ ™Šƒ– ‹• known:

O

B (0,2)

To determine which quadrant A is in, use 4 AOB + r = Ǥ ‹…‡ 2 r equals ° 360 , & ° 2 4 360 AOB + S S ° 360 ° 2 4 2 90 AOB # + S S Ǥ Construct a 45 q -45 q -90 q triangle that describes the position of A in terms of its sides x and y , which are equal : ° 45

A ( x,y )

r =2

s

O 45˚

B (0,2)

s