What are the coordinates of the point on the directed line segment from (- 3, - 9) to (4, 5) that partitions the segment into a ratio of 5 to 2?

(0,-1)

Step-by-step explanation:

Let the ends of the line segments be A(-4,3) and B(5,-6).

Ratio=4:5

By the concept of cordinate geometry,

x=(mx2+nx1)/(m+n)

y=(my2+ny1)/(m+n)

where m and n is the ratio m:n.

So, here the cordinates are

x={4(5)+5(-4)}/(4+5)

x=(20–20)/9

x=0

y={4(-6)+5(3)}/9

y={-24+15}/9

y=(-9)/9

y=(-1)

Therefore the cordinates of the point that divides the given line segment in the ratio 4 : 5 is (0,-1)

:)

A.

B. Point Slope Form: and Slope-Intercept Form:

C. Independent

D.

Step-by-step explanation:

Given 2 points on Sidewalk 1: and .

Given 2 points on Sidewalk 2: and

Where,

m is the slope, and [NOTE: is point 1 and is point 2]

b is the y-intercept [point where the line crosses the y-axis]

Where,

m is the slope, and

is point 1

A.

Slope-Intercept from is given by

Finding m using formula above gives us:

Plugging in any one point, let us substitute , in x and y respectively gives us value of b:

Now we can write:

B.

Solving for m for sidewalk 2 using points above and slope formula, we get:

Point-Slope form using formula above:

Rearranging this in slope-intercept form, we have:

C.

2 lines DOES NOT have any solution when:

1. They are the same line [coefficients of one line are multiple of coefficient of another line ]

2. They are parallel [ when slope of one line is equal to slope of another line ]

Here, none of these occurs, so we HAVE a solution.

Hence, the system of equations are said to be INDEPENDENT.

D.

Since, the 2 equations have a solution [they have an intersection point], let's solve for the intersecting point.

We have the equations and

We set both of them equal [y=y] and solve for x:

Now substitute this value of x into either equation to get y. Let's do it on equation 1:

So, point of intersection is