Question

Can someone help me

Answer 1

1) The distance between points is:
`√(290)`

Option B is correct option.

2) The distance between points is:
`√(10)`

Option A is correct option.

Explanation:

Find the distance between points

Question 1

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

The formula used is:
`Distance=√((x_2-x_1)^2+(y_2-y_1)^2)`

We have
`x_1=8, y_1=-5,x_2=-3,y_2=8`

Putting values and finding distance

`Distance=√((x_2-x_1)^2+(y_2-y_1)^2)\\Distance=√((-3-8)^2+(8-(-5))^2)\\Distance=√((-11)^2+(8+5)^2)\\Distance=√((-11)^2+(13)^2)\\Distance=√(121+169)\\Distance=√(290)`

So, the distance between points is:
`√(290)`

Option B is correct option.

Question 2

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

The formula used is:
`Distance=√((x_2-x_1)^2+(y_2-y_1)^2)`

We have
`x_1=-1, y_1=6,x_2=-4,y_2=-7`

Putting values and finding distance

`Distance=√((x_2-x_1)^2+(y_2-y_1)^2)\\Distance=√((-4-(-1))^2+(-7+6)^2)\\Distance=√((-4+1)^2+(-1)^2)\\Distance=√((-3)^2+(-1)^2)\\Distance=√(9+1)\\Distance=√(10)`

So, the distance between points is:
`√(10)`

Option A is correct option.