Question

point d lies on bc such that bd:cd is 1:5. graph d.

Explanation:

1. First, assume the coordinates of \(B=(x_1,y_1)\) and \(C=(x_2,y_2)\). From the graph, \(B = (- 6,-4)\) and \(C=(5,8)\).

• The section - formula for a point \(D=(x,y)\) that divides the line - segment joining \(B(x_1,y_1)\) and \(C(x_2,y_2)\) 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 \(n = 5\), \(x_1=-6\), \(y_1=-4\), \(x_2 = 5\), and \(y_2 = 8\).

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

• \(x=\frac{1\times5+5\times(-6)}{1 + 5}=\frac{5-30}{6}=\frac{-25}{6}\approx - 4.17\).

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

• \(y=\frac{1\times8+5\times(-4)}{1 + 5}=\frac{8 - 20}{6}=\frac{-12}{6}=-2\).

So, the coordinates of point \(D\) are \((-\frac{25}{6},-2)\). To graph \(D\), locate the point on the coordinate - plane where \(x =-\frac{25}{6}\approx - 4.17\) and \(y=-2\).

Step1: Identify coordinates of B and C

\(B=(-6,-4)\), \(C=(5,8)\)

Step2: Apply section - formula for x - coordinate

\(x=\frac{1\times5 + 5\times(-6)}{1+5}=\frac{5 - 30}{6}=-\frac{25}{6}\)

Step3: Apply section - formula for y - coordinate

\(y=\frac{1\times8+5\times(-4)}{1 + 5}=\frac{8-20}{6}=-2\)

Answer:

The coordinates of point \(D\) are \((-\frac{25}{6},-2)\)