QuestionAugust 25, 2025

The coordinates of the endpoints of overline (CD) are C(-6,-1) and D(6,5) Point E is on overline (CD) and divides it such that CE:DE is 1:5 What are the coordinates of E? Write your answers as integers or decimals. (square ,square )

The coordinates of the endpoints of overline (CD) are C(-6,-1) and D(6,5) Point E is on overline (CD) and divides it such that CE:DE is 1:5 What are the coordinates of E? Write your answers as integers or decimals. (square ,square )
The coordinates of the endpoints of overline (CD) are C(-6,-1) and D(6,5) Point E is on overline (CD) and divides it such that CE:DE is 1:5 What are the coordinates of E? Write your answers as integers or decimals. (square ,square )

Solution
4.7(256 votes)

Answer

(-4, 0) Explanation 1. Calculate the ratio The given ratio is 1:5, so CE = \frac{1}{6} of CD and DE = \frac{5}{6} of CD. 2. Use Section Formula **Section formula** for internal division: If a point divides a line segment in the ratio m:n, then its coordinates are \left(\frac{mx_2 + nx_1}{m+n}, \frac{my_2 + ny_1}{m+n}\right). 3. Apply the Section Formula Here, m=1, n=5, (x_1, y_1) = (-6, -1), (x_2, y_2) = (6, 5). Coordinates of E: \left(\frac{1 \cdot 6 + 5 \cdot (-6)}{1+5}, \frac{1 \cdot 5 + 5 \cdot (-1)}{1+5}\right). 4. Simplify the Expression x-coordinate: \frac{6 - 30}{6} = \frac{-24}{6} = -4. y-coordinate: \frac{5 - 5}{6} = \frac{0}{6} = 0.

Explanation

1. Calculate the ratio<br /> The given ratio is $1:5$, so $CE = \frac{1}{6}$ of $CD$ and $DE = \frac{5}{6}$ of $CD$.<br />2. Use Section Formula<br /> **Section formula** for internal division: If a point divides a line segment in the ratio $m:n$, then its coordinates are $\left(\frac{mx_2 + nx_1}{m+n}, \frac{my_2 + ny_1}{m+n}\right)$.<br />3. Apply the Section Formula<br /> Here, $m=1$, $n=5$, $(x_1, y_1) = (-6, -1)$, $(x_2, y_2) = (6, 5)$. <br /> Coordinates of E: $\left(\frac{1 \cdot 6 + 5 \cdot (-6)}{1+5}, \frac{1 \cdot 5 + 5 \cdot (-1)}{1+5}\right)$.<br />4. Simplify the Expression<br /> $x$-coordinate: $\frac{6 - 30}{6} = \frac{-24}{6} = -4$.<br /> $y$-coordinate: $\frac{5 - 5}{6} = \frac{0}{6} = 0$.
Click to rate:

Similar Questions