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Answer:

1) The distance between points is: [tex]\sqrt{290}[/tex]

Option B is correct option.

2) The distance between points is: [tex]\sqrt{10}[/tex]

Option A is correct option.

Step-by-step explanation:

Find the distance between points

Question 1

(8,-5),(-3,8)

The formula used is: [tex]Distance=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

We have [tex]x_1=8, y_1=-5,x_2=-3,y_2=8[/tex]

Putting values and finding distance

[tex]Distance=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\\Distance=\sqrt{(-3-8)^2+(8-(-5))^2}\\Distance=\sqrt{(-11)^2+(8+5)^2}\\Distance=\sqrt{(-11)^2+(13)^2}\\Distance=\sqrt{121+169}\\Distance=\sqrt{290}[/tex]

So, the distance between points is: [tex]\sqrt{290}[/tex]

Option B is correct option.

Question 2

(-1,6),(-4,-7)

The formula used is: [tex]Distance=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

We have [tex]x_1=-1, y_1=6,x_2=-4,y_2=-7[/tex]

Putting values and finding distance

[tex]Distance=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\\Distance=\sqrt{(-4-(-1))^2+(-7+6)^2}\\Distance=\sqrt{(-4+1)^2+(-1)^2}\\Distance=\sqrt{(-3)^2+(-1)^2}\\Distance=\sqrt{9+1}\\Distance=\sqrt{10}[/tex]

So, the distance between points is: [tex]\sqrt{10}[/tex]

Option A is correct option.

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