Question

partitioning a segment practice
complete this assessment to review what youve learned. it will not count toward your grade.
given points ( a(1,1) ) and ( b(7,-2) ), determine the coordinates of point ( m ) on ( overline{ab} ) such that the ratio of ( am ) to ( mb ) is ( 1:5 ). write your responses as decimal values (if necessary) to the tenths place. (1 point)
( m ) is located at (
check answer remaining attempts 3

Explanation:

Step1: Use the section formula

If a point \(M(x,y)\) divides the line - segment joining \(A(x_1,y_1)\) and \(B(x_2,y_2)\) in the ratio \(m:n\), then \(x=\frac{mx_2 + nx_1}{m + n}\) and \(y=\frac{my_2+ny_1}{m + n}\). Here, \(m = 1\), \(n = 5\), \(x_1=1\), \(y_1 = 1\), \(x_2=7\), \(y_2=-2\).

Step2: Calculate the \(x\) - coordinate

Substitute the values into the \(x\) - coordinate formula:
\(x=\frac{1\times7+5\times1}{1 + 5}=\frac{7 + 5}{6}=\frac{12}{6}=2\)

Step3: Calculate the \(y\) - coordinate

Substitute the values into the \(y\) - coordinate formula:
\(y=\frac{1\times(-2)+5\times1}{1 + 5}=\frac{-2 + 5}{6}=\frac{3}{6}=0.5\)

Answer:

\((2,0.5)\)