60 POINTS AND WILL MARK BRAINLIEST Given the points A(-1,2) and B(7,14), find the coordinates of the Point P on the directed line segment AB that partitions AB in the ratio 1:3. In the above problem, what is the value of a/(a+b)?

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The line APB is a line such that AP/PB= 1/3. From the points A and B that we have we can find the distance between those points using the formula d= [(y2-y1)^2=(x2-x1)^2]^1/2

d= 4 (13)^(1/2)

Now the ratio is 1:3. AP= sq rt(13) and PB= 3 sq rt(13)

Using mid point formula the mid point of AB (say Q) = [(-1+7)/2,(2+14)/2]= (3,8).  

Hence the mid point of AQ is P which can found out again using the mid point formula  

P= [(-1+3)/2,(2+8)/2]= (1,5)

Final P=(1,5)

Step-by-step explanation:

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Step-by-step explanation:

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18 units²

step-by-step explanation:

first let's find altitude bd using the distance formula

d = √((y₂ - y₁)² + (x₂ - x₁)²)

bd = √((0 - -3)² + (0 - 3)²)

bd = √18

given the placement of points a and c, we can denote that point d bisects segment ac.

we will call ac the base.

using the distance formula

ac = √((0 - 6)² + (-6 - 0)²)

ac = √72

knowing our base and our height, we can plug these into our triangle area formula

area = (b * h)/2

area = (√18 * √72) / 2

area = (√1296) / 2

area = 36 / 2

area = 18 units²

-1/4 > -1 2/3. -1/4 is greater than -1 2/3 because it is closer to 0 on the number line.