Question

The point (2,−11) is reflected in the x-axis and then reflected in the line y=x to get the point (a,b). What is the value of a+b?

Answer 1

13 is the answer.
You want the detail?

Answer 2

who cares about the answer , all i want is the detail

Answer 3

yes, detail about your answer give me more confidence

Answer 4

When you reflect a point in the x- axis the x co-ordinate stays the same and the y co-ordinate becomes negative:

So (2, -11) will become (2, 11).

Now there are 2 ways to proceed. You can either say that when you reflect a point in y=x you swap the co-ordinates, so the answer will be (11, 2), or you can go for a more complete answer:

When we reflect (2, 11) in the line y=x to get (a, b), the mid point of (a, b) and (2, 11) will lie on the line y=x. So the point:
\[(\frac{a+2}{2}, \frac{b+11}{2})\]
Will lie on the line y=x. Hence we have:
\[\frac{a+2}{2} = \frac{b+11}{2}\]
and so
\[a+2=b+11\]
So:
\[a=b+9 \]
Let's call this equation 1. Now, another piece of information we can gain: the slop between the points (a, b) and (2, 11) will be -1. So use the gradient formula:
\[\frac{b-11}{a-2}=-1\]
\[b-11=2-a\]
\[b=13-a\]
Substituting this into equation 1 we have:
\[a=(13-a)+9\]
\[2a=22\]
\[a=11\]
Now substituting a=11 into b=13-a gives b=2. So (a, b)=(11, 2) and a+b=13.

Answer 5

@irudayadhason is there anything I can explain more for you?

Answer 6

no.i am going to type a new question please answer that, i got it for this question

Answer 7

please don't reply for this question, it's taking a long time i want to type my next question.

Answer 8

Okidoke

Answer 9

please demitris don't reply for this question, it's taking a long time i want to type my next question