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Given the points R(6,-2) and T(-9,-7), find the coordinates of point S on RT such that the ratio of RS to ST is 3:2

Sagot :

R(6,-2)

T(-9,-7)

RS:ST = 3:2

To find the x coordinate of the point S we use the next equation:

[tex]X_S=X_R-r(X_R-X_T)[/tex]

Where the r is the ratio expressed as a fraction

[tex]r=\frac{\text{3}}{5}[/tex]

Then:

[tex]X_S=6_{}-\frac{3}{5}(6_{}-(-9)_{})[/tex][tex]X_S=6-\frac{3}{5}(6+9)=6-\frac{3}{5}(15)=6-\frac{45}{5}=6-9=-3[/tex]

Then the y coordinate of the point S is determined by:

[tex]Y_S=Y_R-r(Y_R-Y_T)[/tex][tex]Y_S=-2-\frac{3}{5}(-2-(-7))[/tex][tex]Y_S=-2-\frac{3}{5}(5)=-2-\frac{15}{5}=-2-3=-5[/tex]Then so, the coordinated of the point S are:(-3 , - 5)
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