Question

find the distance between the two points rounding to the nearest tenth (if necessary). (6, 4) and (2, 9)

Explanation:

Step1: Recall distance formula

The distance \( d \) between two points \((x_1,y_1)\) and \((x_2,y_2)\) is given by \( d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2} \). Here, \( x_1 = 6,y_1 = 4,x_2 = 2,y_2 = 9 \).

Step2: Substitute values into formula

Substitute the values: \( d=\sqrt{(2 - 6)^2+(9 - 4)^2}=\sqrt{(- 4)^2+5^2} \)

Step3: Simplify the expression

Simplify the squares: \( \sqrt{16 + 25}=\sqrt{41} \)

Step4: Calculate the numerical value

\( \sqrt{41}\approx6.4 \) (rounded to the nearest tenth)

Answer:

\( 6.4 \)