1. Find the distance between $$ \mathrm{P}(7,-4) $$ and line 1 , given by the equation $$ x=-3 $$

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The distance between $$ P(7, -4) $$ and the line $$ x = -3 $$ is 10. To find the distance between the point $$ P(7, -4) $$ and the line given by the equation $$ x = -3 $$, we first note that this line is a vertical line where all points on the line have an $$ x $$-coordinate of $$-3$$. The distance from a point to a vertical line can be calculated by finding the absolute difference between the $$ x $$-coordinate of the point and the $$ x $$-coordinate of the line. The $$ x $$-coordinate of point $$ P $$ is $$ 7 $$, and the $$ x $$-coordinate of the line is $$-3$$. Therefore, the distance $$ d $$ is given by: $$ d = |x_P - x_{\text{line}}| = |7 - (-3)| = |7 + 3| = |10| = 10 $$ Thus, the distance between the point $$ P(7, -4) $$ and the line $$ x = -3 $$ is $$ \boxed{10} $$.

1. Find the distance between \( \mathrm{P}(7,-4) \) and line 1 , given by the equation \( x=-3 \)

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1. Find the distance between \( \mathrm{P}(7,-4) \) and line 1 , given by the equation \( x=-3 \)

UpStudy ThothAI Solution

Step-by-step Solution

Quick Answer

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