2 years ago

1. Is an arithmetic sequence a function?

1 answer:

4 0

Yes, always.

A sequence is a function that takens a positive integer and maps it some other number. For any integer you plug into the sequence, you only ever get one output.

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Point F is at (0, -10) and point H is at (-6, 5). Find the coordinates of point G on line segment FH such that the ratio of FG t

Tanya [424]

Answer:

G(x,y)=(-4,0)

Step-by-step explanation:

We use the section formula:

$(x,y)=\left(\dfrac{mx_2+nx_1}{m+n}, \dfrac{my_2+ny_1}{m+n}\right)$

Given:

$F(x_1,y_1)=(0, -10)\\H(x_2,y_2)=(-6, 5)\\FG:GH=m:n=2:1$

We substitute the values to get:

$G(x,y)=\left(\dfrac{2*-6+1*0}{2+1}, \dfrac{2*5+1*-10}{2+1}\right)\\=\left(\dfrac{-12}{3}, \dfrac{10-10}{3}\right)\\=\left(\dfrac{-12}{3}, \dfrac{0}{3}\right)\\\\G(x,y)=(-4,0)$