Question

1. given two endpoints of a segment y(4, -2) and z(8, 3). find the coordinate p on yz that is 3/4 of the distance from y to z.

$x_p=x_b + f(x_e - x_b)$

$y_p=y_b + f(y_e - y_b)$

$p = ( )$

Explanation:

Step1: Identify the values

Let \(Y(4,-2)\) be \((x_B,y_B)\) and \(Z(8,3)\) be \((x_E,y_E)\), and \(F = \frac{3}{4}\).

Step2: Calculate the x - coordinate of P

\[

$$\begin{align*} x_P&=x_B + F(x_E - x_B)\\ &=4+\frac{3}{4}(8 - 4)\\ &=4+\frac{3}{4}\times4\\ &=4 + 3\\ &=7 \end{align*}$$

\]

Step3: Calculate the y - coordinate of P

\[

$$\begin{align*} y_P&=y_B + F(y_E - y_B)\\ &=-2+\frac{3}{4}(3+ 2)\\ &=-2+\frac{3}{4}\times5\\ &=-2+\frac{15}{4}\\ &=\frac{-8 + 15}{4}\\ &=\frac{7}{4} \end{align*}$$

\]

Answer:

\((7,\frac{7}{4})\)