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Algebra
Question

Find the coordinate, T, that divides AB into a rat...

Find the coordinate, T, that divides AB into a ratio of 3:1 if A is at (-1, -6) and B is at (-5, 2).

Find the coordinate of the indicated point on the coordinate plane. Use either formula. Coordinates of point which partitions a directed line segment \( A B \) at the ratio of \( a : b \) from \( A ( x _ { 1 } , y _ { 1 } ) \) to \( B ( x _ { 2 } , y _ { 2 } ) \) 

\( ( x , y ) = ( \frac { b x _ { 1 } + a x _ { 2 } } { b + a } , \frac { b y _ { 1 } + a y _ { 2 } } { b + a } ) \) 

OR 

\( ( x , y ) = ( x _ { 1 } + \frac { a } { a + b } ( x _ { 2 } - x _ { 1 } ) , y _ { 1 } + \frac { a } { a + b } ( y _ { 2 } - y _ { 1 } ) ) \) 

Find the coordinate, \( T , \) that divides \( AB \) into a ratio of \( 3 : 1 \) if \( A \) is at \( ( - 1 , - 6 ) \) and \( B \) is at \( ( - 5,2 )\) .

Answer

(-4, 0)

Solution
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