Question

orthe coordinates of the endpoints of lm are l(5,17) and m(15,12). point n is on lm and divides it such that ln:mn is 2:3.what are the coordinates of n?

Answer 1

LM = √((5 - 15)² + (17 - 12)²) = √((-10)² + 5²)

= √(100 + 25) = √125 = 5√5

LN = √((x - 5)² + (y - 17)²) = 2√5

NM = √((x - 15)² + (y - 12)²) = 3√5

x² - 10x + 25 + y² - 34y + 289 = 20

x² - 10x + y² - 34y = -294

x² - 30x + 225 + y² - 24y + 144 = 45

x² - 30x + y² - 24y = -324

x² - 10x + y² - 34y = -294

x² - 30x + y² - 24y = -324

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20x - 10y = 30

2x - y = 3

y = 2x - 3

x² - 30x + (2x - 3)² - 24(2x - 3) = -324

x² - 30x + 4x² - 12x + 9 - 48x + 72 = -324

5x² - 90x + 405 = 0

x² - 18x + 81 = 0

(x - 9)² = 0

x = 9, y = 2(9) - 3 = 15

The coordinates of N are (9, 15).