Question

refer to the coordinate grid. find point y on cd such that the ratio of dy to yc is 2:1. a) (1, 3/14) b) (-1, 3/14) c) (3, 14/3) d) (-3, -1)

Explanation:

Step1: Recall section - formula

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

Step2: Assume coordinates of \(D\) and \(C\)

Let's assume \(D(x_1,y_1)\) and \(C(x_2,y_2)\). From the graph, if we assume \(D(-3,-1)\) and \(C(3,1)\).

Step3: Calculate \(x\) - coordinate of \(Y\)

Using the formula \(x=\frac{mx_2+nx_1}{m + n}\), substitute \(m = 2\), \(n = 1\), \(x_1=-3\), \(x_2 = 3\). Then \(x=\frac{2\times3+1\times(-3)}{2 + 1}=\frac{6 - 3}{3}=1\).

Step4: Calculate \(y\) - coordinate of \(Y\)

Using the formula \(y=\frac{my_2+ny_1}{m + n}\), substitute \(m = 2\), \(n = 1\), \(y_1=-1\), \(y_2 = 1\). Then \(y=\frac{2\times1+1\times(-1)}{2 + 1}=\frac{2 - 1}{3}=\frac{1}{3}\).

Answer:

A. \((1,\frac{1}{3})\)