Question

point e lies on cd such that ce:de is 1:4. graph e.

Explanation:

1. First, assume the coordinates of point \(C=(x_1,y_1)\) and point \(D=(x_2,y_2)\). From the graph, \(C = (- 6,-7)\) and \(D=(4, - 2)\).

• The section - formula for a point \(E=(x,y)\) that divides the line - segment joining \(C(x_1,y_1)\) and \(D(x_2,y_2)\) in the ratio \(m:n\) is given by:
• \(x=\frac{mx_2+nx_1}{m + n}\) and \(y=\frac{my_2+ny_1}{m + n}\). Here, \(m = 1\) and \(n = 4\).

1. Calculate the \(x\) - coordinate of point \(E\):

• Substitute \(x_1=-6\), \(x_2 = 4\), \(m = 1\), and \(n = 4\) into the \(x\) - coordinate formula.
• \(x=\frac{1\times4+4\times(-6)}{1 + 4}=\frac{4-24}{5}=\frac{-20}{5}=-4\).

1. Calculate the \(y\) - coordinate of point \(E\):

• Substitute \(y_1=-7\), \(y_2=-2\), \(m = 1\), and \(n = 4\) into the \(y\) - coordinate formula.
• \(y=\frac{1\times(-2)+4\times(-7)}{1 + 4}=\frac{-2-28}{5}=\frac{-30}{5}=-6\).

1. To graph point \(E\):

• Locate the point \((-4,-6)\) on the coordinate - plane. Start at the origin, move 4 units to the left along the \(x\) - axis (because the \(x\) - coordinate is \(-4\)) and then 6 units down along the \(y\) - axis (because the \(y\) - coordinate is \(-6\)) and mark the point.

Step1: Identify coordinates of C and D

\(C=(-6,-7)\), \(D=(4,-2)\)

Step2: Calculate x - coordinate of E

\(x=\frac{1\times4 + 4\times(-6)}{1+4}=\frac{4 - 24}{5}=-4\)

Step3: Calculate y - coordinate of E

\(y=\frac{1\times(-2)+4\times(-7)}{1 + 4}=\frac{-2-28}{5}=-6\)

Step4: Graph the point

Locate \((-4,-6)\) on the plane

Answer:

Graph the point \(E(-4,-6)\)