Simple distance formula question:?

Question

I'm doing a precalc review, and for some reason, I keep getting this wrong. The question is:

"Find x so that the distance between the points (6,-1) and (x,9) is 12."

No matter what I do, my answer is always off by about 2. Can someone tell me HOW to solve this please? Thank you!

Answer 1

Find x so that the distance between the points (6,-1) and (x,9) is 12.

Using the distance formula we know that
sqrt((x-6)^2+(9--1)^2) = 12

Square both sides to get
(x-6)^2+(9--1)^2 = 144

Simplify the left side
(x-6)^2+100 = 144

Subtract 100 from each side
(x-6)^2 = 44

Take the sqaure root of both sides
x-6 = + or - sqrt(44)

Add 6 to both sides and simplify the sqrt of 44
x = 6+or - 2sqrt(11)

x is approximately 12.63 or-0.63

Answer 2

In order to do this, use the distance formula. This formula states for two points, (x,y) and (m, n), the distance between these points are:

Distance = √((n - y)² + (m - x)²)

Plug in your coordinates to this equation:

12 = √((n - y)² + (m - x)²)
= 12= √((9 - (-1))² + (x - 6)²)

Now subtract -1 from 9:

12 = √((9 - (-1))² + (x - 6)²)
= 12 = √((10)² + (x - 6)²)

Next, square 10:

12 = √((10)² + (x - 6)²)
= 12 = √(100 + (x - 6)²)

Because the square root of 144 equals 12, (x - 6) must equal √44 or -√44:

x - 6 = √44 or -√44
x = √44 or -√44 + 6

This is your answer: x = 6 + or - √44 or x = 6 + or - 2√11. (2√11 = √44)

Hope this helps!

Answer 3

Sounds like you figured the distance from-1 to 9 to be 8, when it should be 10.

The distance 12 is the hypoteneuse of a right triangle.
The distances of the other 2 sides are x-6 and 9-(-1)
By the Pythagorean Theorem,
12^2 = (x-6)^2 + 10^2
144 = x^2 -12x +36 +100
x^2 -12x -8 =0
Now I can"t eyeball this to get two tidy factors, so I'll use the quadratic formula, OR I'll factor by completing the square. Both ways will yield identical answers. I'll go the "complete the square" route

x^2 -12x -8=0
x^2-12x =8
x^2-12x+36 = 8+36
(x-6)^2 =44
x-6 = sq.rt.44
x-6 = rt(4)rt11
x-6= + or - 2rt11
x=6+2rt11 or 6-2rt11
x=6+2(3.32) or 6-2(3.32)
x=6+6.64 or 6-6.64
x=12.64 or -0.64

Bear in mind that we just solved for a co-ordinate point for x, not for a distance value
Let's check our answer.

(6-12.64)^2 + (-1-9)^2 =?
(-6.64)^2+ (-10)^2 =?
44.09 + 100= 144
Close enough for Government work! 12.64 works

Now, what about -0.64?
(-0.64-6)^2 +(9-(-1))^2 =?
(-6.64)^2 +10^2=?
44.09+100=144

You therefore have 2 workable solutions: x can be
12.64 or -0.64 and the co-ordinates are (12.64,9) and (-0.64,9)

Your error of about 2 brings back not so fond memories- in my final year of Engineering I said, on a final exam, that there were 12ft. in an inch!
Good luck to you.

Answer 4

d ² = (x - 6) ² + (9 + 1) ²
12 ² = (x - 6) ² + 100
(x - 6) ² = 44
x - 6 = ± √44
x - 6 = ± 2√11
x = 6 ± 2√11

Answer 5

♣ thus 12^2 = (x-6)^2 +(9+1)^2; 144=(x-6)^2 +100,
hence x-6=±2√11, x=6±2√11;