Question

select the correct answer.

what is the approximate distance between points t and u? round your answer to the nearest hundredth.

Explanation:

Identify coordinates of points T and U

We locate the coordinates of points \(T\) and \(U\) from the given coordinate plane.
Point \(T\) is located at \(x = 1\) and \(y = -1\), so its coordinates are:

$$T(1, -1)$$

Point \(U\) is located at \(x = 2\) and \(y = -4\), so its coordinates are:

$$U(2, -4)$$

Apply the distance formula

To find the distance \(d\) between two points \((x_1, y_1)\) and \((x_2, y_2)\), we use the Distance Formula:

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

Substituting the coordinates of \(T(1, -1)\) and \(U(2, -4)\):

$$d = \sqrt{(2 - 1)^2 + (-4 - (-1))^2}$$

Simplify the expression

We calculate the differences inside the parentheses:

$$x_2 - x_1 = 2 - 1 = 1$$

$$y_2 - y_1 = -4 + 1 = -3$$

Now, square these values:

$$1^2 = 1$$

$$(-3)^2 = 9$$

Add the squared values together:

$$d = \sqrt{1 + 9} = \sqrt{10}$$

Calculate the approximate value

We find the square root of \(10\) and round it to the nearest hundredth:

$$\sqrt{10} \approx 3.162277...$$

Rounding to two decimal places gives:

$$d \approx 3.16$$

Answer:

3.16