Question

how to in what does the line of the equation 4x +5y=21divide the line segment joining the points [-2,3]and[4,5]?

Answer 1

Answer:

( $\frac{8}{17}$ , $\frac{65}{17}$ ) , ratio 5 : 7

Step-by-step explanation:

m = ($y_{2}$ - $y_{1}$) / ($x_{2}$ - $x_{1}$)

y - $y_{1}$ = m(x - $x_{1}$)

~~~~~~~~~~

m = $\frac{3-5}{-2-4}$ = $\frac{1}{3}$

y - 5 = $\frac{1}{3}$ (x - 4)

y = $\frac{1}{3}$ x + $\frac{11}{3}$ ⇔ x - 3y = - 11

4x + 5y = 21 ....... (1)

x - 3y = - 11 ...... (2)

(2) × 4 - (1) ⇒ 17y = 65 ⇒ y = $\frac{65}{17}$

y ----> (1)

x - $\frac{65}{17}$ × 3 = - 11 ⇒ x = $\frac{195}{17}$ - $\frac{187}{17}$ ⇒ x = $\frac{8}{17}$

( $\frac{8}{17}$ , $\frac{65}{17}$ )