The coordinates of the three locations are illustrated by line segment ratio
The coordinate of Cristian's house is (13,-1)
The given parameters are:
Jayda = (1,5)
Restaurant = (11,0)
Ratio (m : n) = 5 : 1
Using the line segment ratio, we have:
[tex](x,y) = \frac{1}{m + n}(mx_2 + nx_1 ,my_2 + ny_1)[/tex]
So, the equation becomes
[tex](11,0) = \frac{1}{5 +1}(5 * x_2 + 1 ,5 * y_2 + 5)[/tex]
[tex](11,0) = \frac{1}{6}(5 * x_2 + 1 ,5 * y_2 + 5)[/tex]
Multiply through by 6
[tex](66,0) = (5 * x_2 + 1 ,5 * y_2 + 5)[/tex]
By comparison, we have:
[tex]5 * x_2 + 1 = 66[/tex]
[tex]5 * y_2 + 5 = 0[/tex]
Solve for x2 and y2
[tex]5 * x_2 + 1 = 66[/tex]
[tex]5x_2 = 65[/tex]
[tex]x_2 = 13[/tex]
[tex]5 * y_2 + 5 = 0[/tex]
[tex]5y_2 = -5[/tex]
[tex]y_2 = -1[/tex]
Hence, the coordinate of Cristian's house is (13,-1)
Read more about line segment ratio at:
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