In a AABC, where A(0, 5), B(-2, -3), C (5, 4), the equation of the median through A is given by : (a)In a AABC, where A(0, 5), B(-2, -3), C (5, 4), the equation of the median through A is given by : (a)
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Answer:
Solution
We have,
AB
AP
=
AC
AQ
=
4
3
⇒
AP+PB
AP
=
AQ+QC
AQ
=
4
3
⇒
AP+PB
AP
=
4
3
,
AQ+QC
AQ
=
4
3
⇒4AP=3AP+3PBand4AQ=3AQ+3QC
⇒AP=3PBandAQ=3QC
⇒
PB
AP
=
1
3
and
QC
AQ
=
1
3
⇒PandQdivideABandACrespectivelyinthesameratio3:1
Thus, the coordinates of P and Q are
(
3+1
3×1+1×5
,
3+1
3×5+1×5
)=(2,5)and(
3+1
3×9+1×5
,
3+1
3×1+1×5
)=(8,2)
∴PQ=
(2−8)
2
+(5−2)
2
=
45
=3
5
units
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