Question

point p is located at (-1,5) on the coordinate plane and point q is located at (3,-3). which point lies on pq? (1,1) (2,1) (5,-13) (3,13)

Explanation:

Step1: Find the slope of line PQ

The formula for slope \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Given \(P(-1,5)\) and \(Q(3,-3)\), \(m=\frac{-3 - 5}{3-(-1)}=\frac{-8}{4}=-2\).

Step2: Use the point - slope form \(y - y_1=m(x - x_1)\)

Using point \(P(-1,5)\) and \(m = - 2\), the equation is \(y - 5=-2(x + 1)\), which simplifies to \(y=-2x+3\).

Step3: Check each point

• For \((1,1)\): Substitute \(x = 1\) into \(y=-2x + 3\), \(y=-2\times1+3=1\).
• For \((2,1)\): Substitute \(x = 2\) into \(y=-2x + 3\), \(y=-2\times2+3=-1

eq1\).

• For \((5,-13)\): Substitute \(x = 5\) into \(y=-2x + 3\), \(y=-2\times5+3=-7

eq-13\).

• For \((3,13)\): Substitute \(x = 3\) into \(y=-2x + 3\), \(y=-2\times3+3=-3

eq13\).

Answer:

\((1,1)\)