Mathematics, 20.07.2019 11:10 mickimlvn6128

Given line segment ab with endpoints a(-9, 2) and b(12, 8) what are the coordinated of point c that is partitioned one third from a to b. .

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Check the picture below.

so, from A to B cut at 1/3, simply means, splitting the AB segment into 1+3 equal pieces, and from those four, AB takes 1 piece, and CB takes the other 3 pieces.

$\bf \left. \qquad \right.\textit{internal division of a line segment}
\\\\\\
A(-9,2)\qquad B(12,8)\qquad
\qquad 1:3
\\\\\\
\cfrac{AC}{CB} = \cfrac{1}{3}\implies \cfrac{A}{B} = \cfrac{1}{3}\implies 3A=1B\implies 3(-9,2)=1(12,8)\\\\
-------------------------------\\\\
{ C=\left(\cfrac{\textit{sum of "x" values}}{\textit{sum of ratios}}\quad ,\quad \cfrac{\textit{sum of "y" values}}{\textit{sum of ratios}}\right)}$

$\bf -------------------------------\\\\
C=\left(\cfrac{(3\cdot -9)+(1\cdot 12)}{1+3}\quad ,\quad \cfrac{(3\cdot 2)+(1\cdot 8)}{1+3}\right)
\\\\\\
C=\left(\cfrac{-27+12}{4}~~,~~\cfrac{6+8}{4} \right)\implies C=\left(-\frac{15}{4}~~,~~\frac{7}{2} \right)
\\\\\\
C=\left(-3\frac{3}{4}~~,~~3\frac{1}{2} \right)$

Given line segment ab with endpoints a(-9, 2) and b(12, 8) what are the coordinated of point c that

Given line segment ab with endpoints a(-9, 2) and b(12, 8) what are the coordinated of point c that

Answer from: tacie57

$C(-\dfrac{15}{4},\dfrac{7}{2})$

Step-by-step explanation:

The given endpoints of the line segment AB are A(-9, 2) and B(12, 8).

It is given that point C partitioned one third from A to B. It means point C divide the line segment AB in 1:3.

Section formula:

If a point divides a line segment PQ in m:n, where endpoints are P(x_1,x_2) and Q(x_2,y_2) , then the coordinates of that point are

$(\dfrac{mx_2+nx_1}{m+n},\dfrac{my_2+ny_1}{m+n})$

Using section formula, the coordinates of point C are

$C=(\dfrac{(1)(12)+(3)(-9)}{1+3},\dfrac{(1)(8)+(3)(2)}{1+3})$

$C=(\dfrac{12-27}{4},\dfrac{8+6}{4})$

$C=(\dfrac{-15}{4},\dfrac{14}{4})$

$C=(-\dfrac{15}{4},\dfrac{7}{2})$

Therefore, the coordinates of point C are $(-\dfrac{15}{4},\dfrac{7}{2})$ .

Answer from: Quest

The slope best fit isc. 1/6 mile per hour
What is the slope of the line of best-fit? a. 6 miles per hourb. 12 miles per hourc. 1/6 miles per h

Answer from: Quest

a. we have two

lines: y = 4-x and

y = 8-x^-1

given two simultaneous equations that are both to be

true, then the solution is the points where the lines cross. the intersection is

where the two equations are equal. therefore the solution that works for both

equations is when

4-x = 8-x^-1

this is where the two lines will cross and that is the

common point that satisfies both equations.

b. 4-x = 8-x^-1

x 4-x 8-x^-1

-3 7

8.33

-2 6 8.5

-1 5 9

0 4

1 3

2 2

7.5

3 1 7.67

the table shows that none of the x values from -3 to 3 is

the solution because in no case does

4-x = 8-x^-1

to find the solution we need to rearrange the equation to

find for x:

4-x = 8-x^-1

multiply both sides with x:

4x-x^2 = 8x-1

x^2+4x-1=0

x= -4.236, 0.236

therefore there are two points that satisfies the

equation.

find y:

x=-4.236

y = 4-x = 4 – (-4.236)

= 8.236

y = 8-x^-1 = .236)^-1

= 8.236

x=0.236

y = 4-x = 4 – (0.236) = 3.764

y = 8-x^-1 = 8-(0.236)^-1

= 3.764

thus the two lines cross at 2 points:

(-4.236, 8.236) & (0.236, 3.764)

c. to solve

graphically the equation 4-x = 8-x^-1

we would graph both lines: y = 4-x and y

= 8-x^-1

the point on the graph where the lines cross is the

solution to the system of equations.

just graph the points on part b on a cartesian coordinate

system and extend the two lines. the

solution is, as stated, the point where the two lines cross on the graph.

step-by-step explanation:

mark brainliest!

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