Solve this question? (grade 10) find "a" so that the distance between points (-2,-3) and (-3, a) is equal to 5
[From: ] [author: ] [Date: 12-03-11] [Hit: ]
578363758962410Ask the person to add one more 5-digit number. If he adds 54732, you add below it 45267. Note that you decided the number by subtracting each of his digit from 9. Thus, you now have.......
way that each digit is 9 minus digit above. You now have...
57836
37589
62410
Ask the person to add one more 5-digit number. If he
adds 54732, you add below it 45267. Note that you decided
the number by subtracting each of his digit from 9.
Thus, you now have.....
57836
37589
62410
54732
45267
Next, ask him to add all the number and he gets 257834
Show him the number which you had written as an answer
to this addition earlier in the folded paper and surprise him.
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"the distance between points (-2,-3) and (-3, a) is equal to 5"
Use the distance formula
(-2 - -3)² + (-3 - a)² = 5²
(1) + (a² + 6a + 9) = 25
a² + 6a - 15 = 0
by the quadratic formula
a = [-6 ± √(6² + 4·1·15)]/(2·1)
= [-6 ± √96)]/2
= [-6 ± 4√6)]/2
= -3 ± 2√6
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several people have answered the question but overlooked the question. Question being why your answer was incorrect.
You were using making a mistake by squaring the individual components and adding them and not adding the component and then squaring the resulting number.
so you should be taking (-3 - (-2))^2 and squaring the answer to get 1^2 =1
make sense now?
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use the distance formula
d = √[(x2 - x1)^2 + (y2 - y1)^2]
5 = √[(-3 - (-2))^2 + (a - (-3))^2]
5 = √[(-3 + 2)^2 + (a + 3)^2]
5 = √[(-1)^2 + a^2 + 6a + 9]
5 = √(a^2 + 6a + 10)
25 = a^2 + 6a + 10
0 = a^2 + 6a - 15
solve for a by completing the square or quadratic formula
a^2 + 6a = 15
a^2 + 6a + 9 = 15 + 9
(a + 3)^2 = 24
a + 3 = ± √24
a + 3 = ± 2√6
a = -3 ± 2√6
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√(-3 -(-2))² + (a-(-3))² = √ [(-1)² + (a + 3)²] = √[1 + a² + 6a + 9]
=> 5 = √[a² + 6a + 10]
=> 25 = a² + 6a + 10
=> a² + 6a - 15 = 0
Then, using the quadratic formula we get:
a = (-6 ± √(6² - 4(1)(-15))/2
=> a = (-6 ± √96)/2 = (-6 ± 4√6)/2 = -3 ± 2√6
i.e. a = -3 + 2√6 or -3 - 2√6
:)>
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I think you are right, but just didn't recognise you had the same result 5= √(-3 -(-2))² + (a-(-3))² so 25 = 1 + a² +6a +9 this makes a² + 6a - 15 = 0 Use the quadratic formula and you are there
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