Using analytic geometry, find the coordinates of the point on

Daniell Phillips 2021-12-11 Answered
Using analytic geometry, find the coordinates of the point on the x axis which is equaidistant from A(5, 8) and B(3, 4)
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Expert Answer

trisanualb6
Answered 2021-12-12 Author has 32 answers

Step 1
Given,
A(5, 8), B(3, 4)
Let, Equidistent point, p(x, 0)
So, using distance formula:
(x3)2+(8)2=(x+3)2+(4)2
Both side
x2+2510x+64=x2+9+6x+16
25+64916=10x+6x
16x=64
x=4

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twineg4
Answered 2021-12-13 Author has 33 answers

Step 1
To find the distance between these two points we will use the distance formula
d=(x2x1)2+(y2y1)2
d1=(5x)2+(20)2 and d2=(2x)2+(30)2
We have that d1=d2 so we have:
(5x)2+(20)2=(2x)2+(30)2
Square both sides
((5x)2+(20)2)2=((2x)2+(30)2)2
Transform (5x)2+(20)2 and (2x)2+(30)2 with using rule:
a=a12
(((5x)2+(20)2)12)2=(((2x)2+(30)2)12)2
Apply exponenet rule: (ab)c=abc
((5x)2+(20)2)6{12×2}=((2x)2+(30)2)12×2
Cancel th ecommon term into the exponent.
(5x)2+(20)2+(2x)2+(30)2
Subtract 2-0 and 2-0
(5x)2+22=(2x)2+32
Step 2
Calculate exponents
(5x)

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