Question

refer to the coordinate grid. find x on mn that is 3/4 of the distance from m to n.

Explanation:

1. First, assume the coordinates of \(M\) and \(N\) by looking at the grid:

• Let \(M=( - 5,-4)\) and \(N=(5,4)\).
• The section - formula for a point \(X=(x,y)\) that divides the line - segment joining \(M=(x_1,y_1)\) and \(N=(x_2,y_2)\) 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, \(m = 3\) and \(n = 1\) since \(X\) is \(\frac{3}{4}\) of the distance from \(M\) to \(N\).

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

• Substitute \(x_1=-5\), \(x_2 = 5\), \(m = 3\), and \(n = 1\) into the \(x\) - coordinate formula \(x=\frac{mx_2+nx_1}{m + n}\).
• \(x=\frac{3\times5+1\times(-5)}{3 + 1}=\frac{15 - 5}{4}=\frac{10}{4}=\frac{5}{2}=2.5\).

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

• Substitute \(y_1=-4\), \(y_2 = 4\), \(m = 3\), and \(n = 1\) into the \(y\) - coordinate formula \(y=\frac{my_2+ny_1}{m + n}\).
• \(y=\frac{3\times4+1\times(-4)}{3 + 1}=\frac{12-4}{4}=\frac{8}{4}=2\).

Answer:

The coordinates of \(X\) are \((2.5,2)\)