Question

Highly use distance from point a is approximately 7.1 units. Is the correct answer A, B, C, or D?

Answer 1

Point D

Step-by-step explanation

The distance between two points (x₁, y₁) and (x₂, y₂) is given by the Pythagorean Theorem,

`d=\sqrt[]{(x_1-x_2)^2+(y_1-y_2)^2}`

Let's find the distance between points A and B,

`d_(AB)=\sqrt[]{(1-4)^2+(1-4)^2}=\sqrt[]{(-3)^2+(-3)^2}=\sqrt[]{9+9}=\sqrt[]{18}\approx4.2`

The distance between points A and C is,

`d_(AC)=\sqrt[]{(1-(-3))^2+(1-4)^2}=\sqrt[]{(4)^2+(-3)^2}=\sqrt[]{16+9}=\sqrt[]{25}=5`

And the distance between points A and D is,

`d_(AD)=\sqrt[]{(1-(-4)^2+(1-(-4)^2}=\sqrt[]{(1+4)^2+(1+4)^2}=\sqrt[]{(5)^2+(5)^2}=\sqrt[]{25+25}=\sqrt[]{50}\approx7.1`

Hence, point D is at approximately 7.1 units from point A.