<p>On the number line the distance between the point whose coordinate is a and the point whose coordinate is b is grater than 100.</p>
<p>Can you please tell me why |a|*|b| > 100 is not correct?</p>
<p>(btw * means multiplication)</p>
<p>You need to use the distance formula: [The</a> Distance Formula](<a href=“http://www.purplemath.com/modules/distform.htm]The”>The Distance Formula: What it is and how it works | Purplemath)</p>
<p>However, I’m not sure why the coordinates of the 2 points are symbolized by only one letter; there should be two variables–one for the x-coordinate and one for the y-coordinate. Of course, I could be misunderstanding the question.</p>
<p>No, this is how the question is. It was one of those questions that list 3 options
I
II
III
and then you chose which of them is true/false. However I don’t get why the formula/option i mentioned is incorrect.</p>
<p>And it is an original SAT question.</p>
<p>Pi, the problem says these are points on the number line, not points in the coordinate plane.</p>
<p>The distance between point A and point B on the number line is abs(B - A).</p>
<p>For example, b= 101 and a=.5 is a counterexample: 101 - .5 >100 but 101 * .5 < 100</p>
<p>Oh, um, oops. I forgot about going back to answer the actual question.</p>
<p>Just use a counterexample: B=101, A=0</p>
<p>It should be |a - b| > 100 or |b - a| > 100
Why is your answer wrong? Because you’re multiplying? Why are you multiplying for a question regarding distance on a number line? If you want the distance on a number line, and the distance should be greater than 100, that means the 2 points are more than 100 units APART (key word is “apart”; when you subtract the value of one point on a number line from the value of the other you should get an answer greater than +100 or less than -100). </p>
<p>Example:
a = 150
b = -450</p>
<p>a - b = 150 - (-450) = 600
a is 600 units ahead of b</p>
<p>Example 2:
a = 300
b = 600</p>
<p>a - b = 300 - 600 = -300
-300 isn’t greater than 100, but its absolute value is (absolute value of -300 is 300). That’s why you need the absolute value. b is 300 units more than a, satisfying the condition that the 2 points are more than 100 apart. The reason we get a negative answer is that we’re using a - b, and b is greater. While we get an answer far below 100 without absolute value, it is quite clear, using a number line, that a and b are more than 100 units apart.</p>