Question

NO LINKS!! URGENT HELP PLEASE!!!

Find the distance between the points and graph please

Answer 1

`√(85)\approx 9.23 \; \sf units\;(3\;s.f.)`

`√(74)\approx 8.60\; \sf units\; (3\;s.f.)`

`√(53)\approx 7.28\; \sf units \;(3\;s.f.)`

Explanation:

The distance formula is a mathematical equation used to calculate the distance between two points in a coordinate system.

`\boxed{\begin{minipage}{7.4 cm}\underline{Distance Formula}\\\\$d=√((x_2-x_1)^2+(y_2-y_1)^2)$\\\\\\where:\\ \phantom{ww}$\bullet$ $d$ is the distance between two points. \\\phantom{ww}$\bullet$ $(x_1,y_1)$ and $(x_2,y_2)$ are the two points.\\\end{minipage}}`

To find the distance between each set of two points, substitute the coordinates of the points into the distance formula and solve for d.

The distance between points (-2, 5) and (0, -4) is:

`\begin{aligned}d&=√((0-(-2))^2+(-4-5)^2)\\&=√((2)^2+(-9)^2)\\&=√(4+81)\\&=√(85)\\&\approx 9.23 \; \sf units\;(3\;s.f.)\end{aligned}`

The distance between points (0, -4) and (5, 3) is:

`\begin{aligned}d&=√((5-0)^2+(3-(-4))^2)\\&=√((5)^2+(7)^2)\\&=√(25+49)\\&=√(74)\\&\approx 8.60\; \sf units\; (3\;s.f.)\end{aligned}`

The distance between points (5, 3) and (-2, 5) is:

`\begin{aligned}d&=√((-2-5)^2+(5-3)^2)\\&=√((-7)^2+(2)^2)\\&=√(49+4)\\&=√(53)\\&\approx 7.28\; \sf units \;(3\;s.f.)\end{aligned}`

Answer 2

The distance formula is:

`d = √((x_2 - x_1)^2+ (y_2 - y_1)^2)`

Where
`(x_1, y_1)` and
`(x_2, y_2)`are the coordinates of the two points.

(-2, 5) & (0, -4):

`d = √((0 - (-2))^2+ ((-4) - 5)^2)=√(85)`

So the distance between (-2, 5) and (0, -4) is
`√(85)`.

(0,-4) & (5, 3):

`d = √((5 - 0)^2+ ((3) - (-4))^2)=√(74)`

So the distance between (0,-4) and (5, 3) is
`√(74)`

(5, 3) & (-2, 5):

`d = √((5 - (-2))^2 + ((3) - 5)^2)=√(53)`

So the distance between (5, 3) and (-2, 5) is
`√(53)`.