If #P(x,y)# lies on the interval #A(x_1,y_1), B(x_2,y_2)# such that #AP : PB =a : b#, with a and b positive, show that #x= (bx_1+ax_2) /(b+a)# and #y=(by_1+ay_2)/(b+a)#?
If #P(x,y)# lies on the interval #A(x_1,y_1), B(x_2,y_2)# such that #AP : PB =a : b# , with a and b positive,show that
#x= (bx_1+ax_2) /(b+a)#
and #y=(by_1+ay_2)/(b+a)# ?
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If
and
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2 Answers
See below.
Explanation:
If
also
but
but anyway
so another reading is
resulting in
See the geometric construction to guide you with set up...
Explanation:
From the figure solve for x:
Rearranging and solving for x we have:
Applying the same logic to the ratio: