Find x if the distance between points L(5,-8) and M(x,-3) is 13*
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Let A and B be the two points such that A(3,x) and (−2,−6) respectively.
AB=13 units(Given)
As we know that distance between the two points (x
1
,y
1
) and (x
2
,y
2
) is-
d=
(x
2
−x
1
)
2
+(y
2
−y
1
)
2
Therefore,
AB=
(−2−3)
2
+(−6−x)
2
⇒AB=
25+(36+x
2
+12x)
But given that AB=13 units
∴
25+(36+x
2
+12x)
=13
Squaring both sides, we have
(
25+(36+x
2
+12x)
)
2
=(13)
2
25+36+x
2
+12x=139
x
2
+12x+61−139=0
x
2
+12x−78=0
Now by quadratic formula, we have
x=
2×1
−12±
(12)
2
−4(−78)(1)
⇒x=
2
−12±
144+312
⇒x=
2
−12±
456
⇒x=−6±
114
Hence the value of x is (−6+
114
) or (−6−
114
).
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