Question

Find the distance between point P and line ℓ.

Answer 1

The distance between the line containing the points (0,-3) and (7,4) and the point P(4,3) is d =√2 units.

What is the distance between a line and a point?

The distance between the line ax +by +c =0 and the point (x₁, y₁) is given by:

$d=\frac{|ax_{1}+by_{1}+c|}{\sqrt{a^2+b^2}}$

Given that, the line passes through the points (0,-3) and (7,4).

The equation of the line is given by:

$y -(-3)=\frac{4-(-3)}{7-0}(x-0)\\\\y+3=x\\\\x-y-3=0$

Now, the distance between the line x - y - 3 = 0 and point (4,3) is:
$d=\frac{|1\times4+(-1)\times3+(-3)|}{\sqrt{1^2 +(-1)^2}}\\\\d=\frac{2}{\sqrt{2}}\\\\d=\sqrt{2}$

Hence, the distance between the line containing the points (0,-3) and (7,4) and the point P(4,3) is d =√2 units.

Learn more about the distance between a line and a point:
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