The-points-A-B-C-D-have-coordinates-7-9-3-4-1-12-and-2-9-find-the-length-of-the-linePQ-where-P-devides-AB-in-the-ratio-2-3-and-devides-CD-in-the-ratio-1-4-

Question Number 54025 by pieroo last updated on 28/Jan/19

The points A, B, C, D have coordinates

(- 7, 9), (3, 4), (1, 12), and (- 2, - 9) .

find the length of the linePQ where P

devides AB in the ratio 2 : 3 and devides

CD in the ratio 1 : - 4 .

Commented by pieroo last updated on 28/Jan/19

I need some help, especially with the

diagram .

Answered by ajfour last updated on 28/Jan/19

Commented by ajfour last updated on 28/Jan/19

x_{P} = \frac{{m x}_{B} + {n x}_{A}}{m + n} = \frac{2 (3) + 3 (- 7)}{5} = - 3

y_{P} = \frac{{m y}_{B} + {n y}_{A}}{m + n} = \frac{2 (4) + 3 (9)}{5} = 7

P (- 3, 7)

x_{Q} = \frac{1 (- 2) + (- 4) (1)}{- 3} = 2

y_{Q} = \frac{1 (- 9) + (- 4) (12)}{- 3} = 19

Q (2, 19)

P Q = \sqrt{{(- 3 - 2)}^{2} + {(7 - 19)}^{2}}

= \sqrt{25 + 144} = 13 u n i t s .

Commented by pieroo last updated on 28/Jan/19

thanks senior

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