Find the distance between each pair points (-5,3) , (-4,-5)?

Mathematics

1 answer:

MrRa [10]3 years ago

4 0

Answer:

$\sqrt{65}$

Step-by-step explanation:

distance between two points:

$d=\sqrt{(x_{2}-x_{1})^{2}+( y_{2}-y_{1})^{2}}$

we have:

$d=\sqrt{(-4-(-5))^{2}+(-5-3)^{2}} \\\\d=\sqrt{1^{2}+(-8)^{2}} \\\\d=\sqrt{65}$

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2 years ago

What is an equation of the line that passes through the points (0, 3) and (5,-3)?

Arisa [49]

Answer:

The equation of the line that passes through the points (0, 3) and (5, -3) is $y = -\frac{6}{5}\cdot x +3$ .

Step-by-step explanation:

From Analytical Geometry we must remember that a line can be formed after knowing two distinct points on Cartesian plane. The equation of the line is described below:

$y = m\cdot x + b$ (Eq. 1)

Where:

$x$ - Independent variable, dimensionless.

$y$ - Dependent variable, dimensionless.

$m$ - Slope, dimensionless.

$b$ - y-Intercept, dimensionless.

If we know that $(x_{1},y_{1}) = (0,3)$ and $(x_{2},y_{2})=(5,-3)$ , the following system of linear equations is constructed:

$b = 3$ (Eq. 2)

$5\cdot m + b = -3$ (Eq. 3)

The solution of the system is: $b = 3$ , $m = -\frac{6}{5}$ . Hence, we get that equation of the line that passes through the points (0, 3) and (5, -3) is $y = -\frac{6}{5}\cdot x +3$ .