Math  /  Geometry

QuestionEXAMPLE 2 Check Your Progress W/CheckPoint COORDINATE GEOMETRY Line nn contains points (2,4)(2,4) and (4,2)(-4,-2). Find the distance between line nn and point B(3,1)B(3,1). A. 4\sqrt{4} or 2 B. 8\sqrt{8} or about 2.83 C. 10\sqrt{10} or about 3.16 D. 36\sqrt{36} or about 6

Studdy Solution
Calculate the distance:
3.1 Substitute the values:
d=31+21+1 d = \frac{|3 - 1 + 2|}{\sqrt{1 + 1}} =42 = \frac{|4|}{\sqrt{2}}
3.2 Simplify the expression:
=42 = \frac{4}{\sqrt{2}} =422 = \frac{4 \sqrt{2}}{2} =22 = 2 \sqrt{2}
3.3 Approximate the distance:
222.83 2 \sqrt{2} \approx 2.83
The distance from point B(3,1) B(3,1) to line n n is approximately 8 \sqrt{8} or about 2.83 2.83 .
The correct answer is:
8 or about 2.83 \boxed{\sqrt{8} \text{ or about } 2.83}

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