Question

which points have the same distance between them as points a and b shown on the coordinate plane? select all that apply. (6,7) and (3, - 2) (-3,8) and (0,3) (-9,-11) and (-4,-8) (3,-6) and (3,0)

Explanation:

1. First, find the distance between points \(A(-4,1)\) and \(B(1, - 2)\) using the distance formula \(d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\):

• Here, \(x_1=-4,y_1 = 1,x_2 = 1,y_2=-2\).
• \(d_{AB}=\sqrt{(1-(-4))^2+(-2 - 1)^2}=\sqrt{(1 + 4)^2+(-3)^2}=\sqrt{25 + 9}=\sqrt{34}\).

1. Then, calculate the distances for each - pair of points:

• For the points \((x_1,y_1)=(6,7)\) and \((x_2,y_2)=(3,-2)\):
• \(d=\sqrt{(3 - 6)^2+(-2 - 7)^2}=\sqrt{(-3)^2+(-9)^2}=\sqrt{9 + 81}=\sqrt{90}

eq\sqrt{34}\).

• For the points \((x_1,y_1)=(-3,8)\) and \((x_2,y_2)=(0,3)\):
• \(d=\sqrt{(0-(-3))^2+(3 - 8)^2}=\sqrt{(0 + 3)^2+(-5)^2}=\sqrt{9 + 25}=\sqrt{34}\).
• For the points \((x_1,y_1)=(-9,-11)\) and \((x_2,y_2)=(-4,-8)\):
• \(d=\sqrt{(-4-(-9))^2+(-8-(-11))^2}=\sqrt{(-4 + 9)^2+(-8 + 11)^2}=\sqrt{25+9}=\sqrt{34}\).
• For the points \((x_1,y_1)=(3,-6)\) and \((x_2,y_2)=(3,0)\):
• \(d=\sqrt{(3 - 3)^2+(0-(-6))^2}=\sqrt{0 + 36}=6

eq\sqrt{34}\).

Answer:

(-3,8) and (0,3); (-9,-11) and (-4,-8)