1. Evaluate each expression when x = -2 and y = 3.

1 answer:

5 0

a) 3(-2) + 4(3) = -6 + 12 = 6

b) 2(-2) -3(3) +5 = -4 -9 + 5 = -8

c) 4(-2) -(3) = -8 -3 = -11

d) -(-2) -2(3) = 4 -6 = -2

e) (1/2)(-2) +(3) = -1 +3 = 2

f) (2/3)(3) -(1/2)(-2) = 2 + 1 = 3

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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

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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:

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