求助一道PREP DS题

yuchenguo

In the xy-plane, does the line with equation y = 3x + 2 contain the point (r, s) ?

 

(1)  (3r + 2 - s)(4r + 9 - s) = 0

 

(2)  (4r - 6 - s)(3r + 2 - s) = 0

标准答案是D

我觉得是C

lzsile

来自于 prep数学详解，你可以在数学那个版下，应该有，用word搜索

In the xy-plane, does the line with equation y = 3x + 2 contain the point (r, s) ?

 

(1)  (3r + 2 - s)(4r + 9 - s) = 0

(2)  (4r - 6 - s)(3r + 2 - s) = 0

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MingLiU","serif"; mso-fareast-language: ZH-TW; mso-bidi-font-family: PMingLiU; mso-ascii-font-family: Tahoma; mso-hansi-font-family: Tahoma;">【答案】C

【思路】

r is the x coordinate, s is the y, so we want to know whether:
s=3r+2
(1)
            Essentially, one equation or the other must be equal to zero (if xy = 0, the x = 0 or y = 0).

either  3r+2-s=0 or 4r+9-s=0,

so:      s=3r+2 or s=4r+9
If it is true that 3r+2-x = 0, then we see that (r.s) must be included in 3r+2 = x, since we have that exact equation. However, it is possible that 4r+9 =s, in which case our equation doesn't have to be 3r+2 = s

In the first case, (r.s) falls in the line. In the second case, (r,s) does not fall in the line.

MingLiU","serif"; mso-fareast-language: ZH-TW; mso-bidi-font-family: PMingLiU; mso-ascii-font-family: Tahoma; mso-hansi-font-family: Tahoma;">無法確定(r,S)MingLiU","serif"; mso-fareast-language: ZH-TW; mso-bidi-font-family: PMingLiU; mso-ascii-font-family: Tahoma; mso-hansi-font-family: Tahoma;">會落在哪一條線…..insufficient because it could be the second case

(2)

either  4r-6-s=0 or 3r+2-s=0,

so:      s=4r-6 or s=3r+2

In the first case, (r.s) falls in the line. In the second case, (r,s) does not fall in the line.

MingLiU","serif"; mso-fareast-language: ZH-TW; mso-bidi-font-family: PMingLiU; mso-ascii-font-family: Tahoma; mso-hansi-font-family: Tahoma;">無法確定(r,S)MingLiU","serif"; mso-fareast-language: ZH-TW; mso-bidi-font-family: PMingLiU; mso-ascii-font-family: Tahoma; mso-hansi-font-family: Tahoma;">會落在哪一條線…..insufficient because it could be the second case

(1)+(2)

y=3x+2 will contain (r,s) only if s=3r+2.
(1) s=3r+2 OR 4r+9. Insuff.
(2) s=4r-6 OR 3r+2. Insuff.
Combining: s=3r+2. Suff. C
MingLiU","serif"; mso-fareast-language: ZH-TW; mso-bidi-font-family: PMingLiU; mso-ascii-font-family: Tahoma; mso-hansi-font-family: Tahoma; mso-highlight: red; mso-font-kerning: 0pt; mso-ansi-language: EN-US; mso-bidi-language: AR-SA;">當(1)MingLiU","serif"; mso-fareast-language: ZH-TW; mso-bidi-font-family: PMingLiU; mso-ascii-font-family: Tahoma; mso-hansi-font-family: Tahoma; mso-highlight: red; mso-font-kerning: 0pt; mso-ansi-language: EN-US; mso-bidi-language: AR-SA;">、(2)MingLiU","serif"; mso-fareast-language: ZH-TW; mso-bidi-font-family: PMingLiU; mso-ascii-font-family: Tahoma; mso-hansi-font-family: Tahoma; mso-highlight: red; mso-font-kerning: 0pt; mso-ansi-language: EN-US; mso-bidi-language: AR-SA;">同時存在時，會出現交集，此交集上的任何一點皆可以滿足題目s=3r+2MingLiU","serif"; mso-fareast-language: ZH-TW; mso-bidi-font-family: PMingLiU; mso-ascii-font-family: Tahoma; mso-hansi-font-family: Tahoma; mso-highlight: red; mso-font-kerning: 0pt; mso-ansi-language: EN-US; mso-bidi-language: AR-SA;">，故選CMingLiU","serif"; mso-fareast-language: ZH-TW; mso-bidi-font-family: PMingLiU; mso-ascii-font-family: Tahoma; mso-hansi-font-family: Tahoma; mso-highlight: red; mso-font-kerning: 0pt; mso-ansi-language: EN-US; mso-bidi-language: AR-SA;">。

yuchenguo

那为什么标准答案写的D呢。。。

prep的答案是不是有点有问题啊？

我百思不得其解呢

melodyflying

选c啦这题

是不是答案有问题啊