Question

1. both points d and u are on the fourth quadrant. if the distance between point d and u is 3 units and d is at (2, -1), which of the following are the coordinates of point u? a) (2, -4) b) (1, -6) c) (4, -1) d) (2, -5)

Explanation:

Step1: Use the distance formula

The distance formula between two points \((x_1,y_1)\) and \((x_2,y_2)\) is \(d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\). Given \(D(2,-1)\) and \(d = 3\).

Step2: Check option A

For \(U(2,-4)\), \(x_1=2,y_1 = - 1,x_2=2,y_2=-4\).
\(d=\sqrt{(2 - 2)^2+(-4+1)^2}=\sqrt{0+(-3)^2}=\sqrt{9}=3\)

Step3: Check option B

For \(U(1,-6)\), \(x_1 = 2,y_1=-1,x_2=1,y_2=-6\)
\(d=\sqrt{(1 - 2)^2+(-6 + 1)^2}=\sqrt{(-1)^2+(-5)^2}=\sqrt{1 + 25}=\sqrt{26}
eq3\)

Step4: Check option C

For \(U(4,-1)\), \(x_1=2,y_1=-1,x_2=4,y_2=-1\)
\(d=\sqrt{(4 - 2)^2+(-1+1)^2}=\sqrt{4+0}=2
eq3\)

Step5: Check option D

For \(U(2,-5)\), \(x_1=2,y_1=-1,x_2=2,y_2=-5\)
\(d=\sqrt{(2 - 2)^2+(-5 + 1)^2}=\sqrt{0+(-4)^2}=4
eq3\)

Answer:

A. \((2,-4)\)