Crushedhanakoidn
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What are the coordinates of the point in the directed line segment from (-2,-8) to (5,-1) that partitions the segment into the ratio of 1 to 6? PLS HELP!!!!

Sagot :

Absor201idn

Answer:

The coordinates of the point X:

  • (x, y) = (-1, -7)

Step-by-step explanation:

Let X be the point.

As the point X is in the directed line segment from (-2,-8) to (5,-1) into the ratio of 1 to 6

i.e.

[tex]\left(x_1,\:y_1\right)\:=\:\left(-2,-8\right)[/tex]

[tex]\left(x_2,\:y_2\right)=\left(5,-1\right)[/tex]

Rise = y₂ - y₁

       [tex]= -1 - (-8)[/tex]

       [tex]= -1 + 8[/tex]

       [tex]= 7[/tex]

Run = x₂ - x₁

      [tex]= 5 - (-2)[/tex]

      [tex]= 5 + 2[/tex]

      [tex]= 7[/tex]

1 : 6 ratio means the point X lies at

[tex]\frac{1}{6+1}=\frac{1}{7}=14\%[/tex]

Thus,

rise for X [tex]=\:7\:\times \:14\%=1[/tex]

run for X [tex]=\:7\:\times \:14\%=1[/tex]

Thus, coordinates of X will be:

[tex]x = -2 + 1 = -1[/tex]

[tex]y = -8 + 1 = -7[/tex]

Therefore, we conclude that:

The coordinates of the point X:

  • (x, y) = (-1, -7)
Raphealnwobiidn

The point (-1, -7) divide the segment from (-2,-8) to (5,-1). in the ratio 1:6.

What is distance?

If a point O(x, y) divides the line segment AB in the ratio of n:m, where the endpoints of the line is A(x₁, y₁) and B(x₂. y₂), the point O is at:

[tex]x=\frac{n}{n+m}(x_2-x_1)+x_1 \\\\y=\frac{n}{n+m}(y_2-y_1)+y_1[/tex]

Given the ratio 1:6, let O(x, y) divide the segment from (-2,-8) to (5,-1). Hence:

[tex]x=\frac{1}{1+6}(5-(-2))+(-2)=-1\\\\y=\frac{1}{1+6}(-1-(-8))+(-8)=-7[/tex]

O = (-1, -7)

The point (-1, -7) divide the segment from (-2,-8) to (5,-1) in the ratio 1:6.

Find out more on distance at: https://brainly.com/question/17273444

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