p varies directly with x and inversely with y. When x = 2, y = 4 and p = 8.
Find p when x = 4 and y=9.
(a) 16
(6) 8
(c) 4
(d) 2
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Given P is equidistant from points A and B
PA=PB .....(1)
and Q is equidistant from points A and B
QA=QB .....(2)
In △PAQ and △PBQ
AP=BP from (1)
AQ=BQ from (2)
PQ=PQ (common)
So, △PAQ≅△PBQ (SSS congruence)
Hence ∠APQ=∠BPQ by CPCT
In △PAC and △PBC
AP=BP from (1)
∠APC=∠BPC from (3)
PC=PC (common)
△PAC≅△PBC (SAS congruence)
∴AC=BC by CPCT
and ∠ACP=∠BCP by CPCT ....(4)
Since, AB is a line segment,
∠ACP+∠BCP=180
∘
Thus, AC=BC and ∠ACP=∠BCP=90
∘
∴,PQ is perpendicular bisector of AB.
Hence proved.
Tusen Takk ✌️❣️
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