If A and B are -2-2-2-4 Find P such that AP-37AB

AP=37AB AP=37[AP+PB] AP=3AP+3PB7 7AP 3AP=3PB or 4AP=3PB or APPB=34 .......... (1) [m=3, n=4] We know mx_2+nx_1m+n, m ...

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Standard X

Mathematics

Arithmetic Mean

If A and ...

Question

If $A$ and $B$ are $(- 2, - 2), (2, - 4)$ Find $P$ such that $A P = \frac{3}{7} A B$

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Solution

$A P = \frac{3}{7} A B$
$A P = \frac{3}{7} [A P + P B]$
$A P = \frac{3 A P + 3 P B}{7}$
$7 A P - 3 A P = 3 P B$
or $4 A P = 3 P B$
or $\frac{A P}{P B} = \frac{3}{4}$ .......... $(1)$
$[m = 3, n = 4]$
We know
$\frac{m x_{2} + n x_{1}}{m + n}, \frac{m y_{2} + n y_{1}}{m + n}$
$\frac{3 (2) + 4 (- 2)}{3 + 4}, \frac{3 (- 4) + 4 (- 2)}{3 + 4}$
$(\frac{6 - 8}{7}, \frac{- 12 - 8}{7})$
$\Rightarrow (\frac{2}{7}, - \frac{20}{7})$ .

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If A and B are (−2,−2),(2,−4) Find P such that AP=37AB

AP=37ABAP=37[AP+PB]AP=3AP+3PB77AP−3AP=3PBor 4AP=3PBor APPB=34 ..........(1)[m=3,n=4]We knowmx2+nx1m+n,my2+ny1m+n3(2)+4(−2)3+4,3(−4)+4(−2)3+4(6−87,−12−87)⇒(27,−207).

If $A$ and $B$ are $(- 2, - 2), (2, - 4)$ Find $P$ such that $A P = \frac{3}{7} A B$