Question

what is the distance between (-1, -6) and (6, 1)?
2√49
49√2
2√7
none of these

Explanation:

Step1: Recall distance formula

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

Step2: Identify coordinates

Here, \( x_1 = -1 \), \( y_1 = -6 \), \( x_2 = 6 \), \( y_2 = 1 \).

Step3: Calculate differences

\( x_2 - x_1 = 6 - (-1) = 7 \), \( y_2 - y_1 = 1 - (-6) = 7 \).

Step4: Substitute into formula

\( d = \sqrt{(7)^2 + (7)^2} = \sqrt{49 + 49} = \sqrt{98} \).

Step5: Simplify \(\sqrt{98}\)

\( \sqrt{98} = \sqrt{49 \times 2} = 7\sqrt{2} \), or also \( \sqrt{98}=\sqrt{49\times2}=\sqrt{49}\times\sqrt{2} = 7\sqrt{2}\), and none of the first three options match \( 7\sqrt{2} \) (since \( 2\sqrt{49}=14 \), \( 49\sqrt{2} \) is too big, \( 2\sqrt{7}\approx5.29 \), but \( 7\sqrt{2}\approx9.899 \) and not equal to any of them).

Answer:

None of these