Question

how far is the point (6,8) from the origin?

Explanation:

Step1: Recall distance formula from origin

The distance \( d \) between a point \( (x,y) \) and the origin \( (0,0) \) is given by the formula \( d = \sqrt{(x - 0)^2+(y - 0)^2}=\sqrt{x^2 + y^2} \). For the point \( (6,8) \), \( x = 6 \) and \( y = 8 \).

Step2: Substitute values into formula

Substitute \( x = 6 \) and \( y = 8 \) into the formula: \( d=\sqrt{6^2 + 8^2} \). Calculate \( 6^2=36 \) and \( 8^2 = 64 \), so \( d=\sqrt{36 + 64} \).

Step3: Simplify the expression

Simplify \( 36+64 = 100 \), then \( d=\sqrt{100} \). Since \( \sqrt{100}=10 \), the distance is 10.

Answer:

10