Question

Segment AB is shown on the graph. Which shows how to find the x-coordinate of the point that will divide into a 2:3 ratio using the formula ? x = (−3−2) + 2 x = (2+3) − 3 x = (−3−2) + 2 x = (2+3) − 3On a coordinate plane, a line has points (negative 2, negative 4) and (4, 2). Point P is at (0, 4). Which points lie on the line that passes through point P and is parallel to the given line? Select three options. (–4, 2) (–1, 3) (–2, 2) (4, 2) (–5, –1)

Answer 1

`(-1,3), (-2,2), (-5,-1)`

Explanation:

1) There's Need for the segment. Reminds me the centroid of a triangle which divides the triangle into two segments in a 2:3 ratio.

2.On a coordinate plane, a line has points (negative 2, negative 4) and (4, 2). Point P is at (0, 4). Which points lie on the line that passes through point P and is parallel to the given line? Select three options. (–4, 2) (–1, 3) (–2, 2) (4, 2) (–5, –1)

1) Let's find the slope of the line
`r` with points
`A(-2,-4) \:and\:B(4,2)`

`m=(2-(-4))/(4-(-2))=(6)/(6)=1`

2) Now the linear coefficient,

`y=mx+b\\0=1(-2)+b\\b=-2`

Then the first line
`r` whose points are
`A(-2,-4) \:and\:B(4,2)` is
`y=x-2`

3) From Analytical Geometry, a Parallel line must have the same slope, so that these lines may never intercept each other just like the graph below. So the slope, the angular coefficient must value the same amount.

`m_1=m_(2) \therefore m_(1)=m_(2)=1`

So, the line
`s` is :

`y=mx+b\\4=1*0+b\\\therefore b=4\\y=x+4`

4) Testing the points

`2=-4+4 \:\\2\\eq 0\\(-1,3)\\3=-1+4\\3=3\\(-2,2)\\2=-2+4\\2=2\\(4,2)\\2\\eq 2+4\\(4,2)\\2\\eq 4+2\\(-5,-1)\\-1=-5+4\\-1=-1`

Answer 2

(–1, 3), (–2, 2) and (–5, –1)

Explanation:

On a coordinate plane, a line has points (-2, -4) and (4, 2). Its slope is:

m = [2 - (-4)]/[4 - (-2)] = 1

To be parallel, both lines have the same slope.

General equation of a line:

y = mx + b

Replacing with m = 1 and Point P (0, 4), we get:

4 = 1(0) + b

4 = b

Therefore, the equation of the line is:

y = x + 4

Replacing x = -4 into the equation:

y = -4 + 4 = 0

Replacing x = -1 into the equation:

y = -1 + 4 = 3 then (-1, 3) lies on the line

Replacing x = -2 into the equation:

y = -2 + 4 = 2 then (-2, 2) lies on the line

Replacing x = 4 into the equation:

y = 4 + 4 = 8

Replacing x = -5 into the equation:

y = -5 + 4 = -1 then (-5, 1) lies on the line