Question

geometry exit ticket 1 - 4: partitioning a line segment mr. ippolito 9/22/2025 1. using the illustrated figure, obtain the point a on the line segment that would partition the line segment into the ratio xa:ay = 5:1

Explanation:

Step1: Recall the section - formula

If a point \(A\) divides the line - segment joining \(X(x_1,y_1)\) and \(Y(x_2,y_2)\) in the ratio \(m:n\), the coordinates of \(A\) (in one - dimensional case, if the line is on a number line) is given by \(A=\frac{mx_2+nx_1}{m + n}\). Here, assume \(X = 5\), \(Y = 17\), \(m = 5\), and \(n = 1\).

Step2: Substitute the values into the formula

\[A=\frac{5\times17+1\times5}{5 + 1}=\frac{85 + 5}{6}=\frac{90}{6}=15\]

Answer:

15