How to find the length of a line with distance formula - Math

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Question

What is the length of a line segment with end points and ?

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Answer

The formula for the length of line is the distance formula, which is very similar to the Pythagorean theorem.

Plug in the given values and solve for the length.

$\sqrt{61}=\sqrt{l^2}$

$\sqrt{61}=l$

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Question

What would be the length of a line with endpoints at and ?

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Answer

The formula for the length of line is the distance formula, which is very similar to the Pythagorean theorem.

Plug in the given values and solve for the length.

$\sqrt{73}=\sqrt{l^2}$

$\sqrt{73}=l$

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Question

If a line has a length of , and the endpoints are and , what is the value of ?

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Answer

The formula for the length of a line, l, is the distance formula, which is very similar to the Pythagorean Theorem.

Note that the problem has already given us a value for the length of the line. That means . Plug in all of the given values and solve for the missing term.

Subtract $\small 16$ from both sides.

$\sqrt{y^2}=\sqrt{9}$

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Question

What line goes through the points and ?

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Answer

Find the slope between the two points:

$m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}=\frac{15-5}{5-(-1)}=\frac{10}{6}=\frac{5}{3}$

Next, use the slope-intercept form of the equation:

or $15=\frac{5}{3}(5)+b$ where $b=\frac{20}{3}$

So the equation becomes $y=\frac{5}{3}x+ \frac{20}{3}$ or in standard form .

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Question

What is the length of a line with endpoints at and ?

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Answer

The formula for the length of a line is very similiar to the pythagorean theorem:

Plug in our given numbers to solve:

$\sqrt{25}=\sqrt{l^2}$

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Question

What is the length of a line with endpoints at and ?

Tap to reveal answer

Answer

The formula for the length of a line is very similiar to the pythagorean theorem:

Plug in our given numbers to solve:

$\sqrt{25}=\sqrt{l^2}$

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Question

What is the distance between points and ?

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Answer

Use the distance formula:

$d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

Plug in the given points:

$d=\sqrt{(12-(-2)))^2+(3-4)^2}$

$d=\sqrt{197}$

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Question

Find the distance between points and .

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Answer

Use the distance formula:

$d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

Substitute the given points into the formula:

$d=\sqrt{(14-2)^2+(-2-(-4))^2}$

$d=\sqrt{148}$

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Question

What is the length of a line with endpoints of and ?

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Answer

The distance formula is just a reworking of the Pythagorean theorem: $l=\sqrt{\Delta x^2+\Delta y^2}$

Expand that.

$l=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

Plug in our given values.

$l=\sqrt{(7-2)^2+(9--4)^2}$

$l=\sqrt{(5)^2+(13)^2}$

$l=\sqrt{25+169}$

$l=\sqrt{194}$

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Question

What is the distance between and ?

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Answer

Let $P_{1}=(1,5)$ and $P_{2} = (6,17)$ .

The distance formula is given by $d = \sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}}$ .

Substitute in the given points:

$d = \sqrt{(6-1)^{2}+(17-5)^{2}}=\sqrt{(5)^{2}+(12)^{2}}=\sqrt{25+144}=\sqrt{169}=13$

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Question

A line segment has endpoints at and . What is the distance of this segment?

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Answer

To find the distance, we use the distance formula: $d^2=\Delta x^2+\Delta y^2$ .

Expand that:

Plug in our given values.

$\sqrt{d^2}=\sqrt{81}$

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Question

What is the length of a line segment with end points and ?

Tap to reveal answer

Answer

The formula for the length of line is the distance formula, which is very similar to the Pythagorean theorem.

Plug in the given values and solve for the length.

$\sqrt{61}=\sqrt{l^2}$

$\sqrt{61}=l$

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Question

What would be the length of a line with endpoints at and ?

Tap to reveal answer

Answer

The formula for the length of line is the distance formula, which is very similar to the Pythagorean theorem.

Plug in the given values and solve for the length.

$\sqrt{73}=\sqrt{l^2}$

$\sqrt{73}=l$

← Didn't Know|Knew It →

Question

If a line has a length of , and the endpoints are and , what is the value of ?

Tap to reveal answer

Answer

The formula for the length of a line, l, is the distance formula, which is very similar to the Pythagorean Theorem.

Note that the problem has already given us a value for the length of the line. That means . Plug in all of the given values and solve for the missing term.

Subtract $\small 16$ from both sides.

$\sqrt{y^2}=\sqrt{9}$

← Didn't Know|Knew It →

Question

What line goes through the points and ?

Tap to reveal answer

Answer

Find the slope between the two points:

$m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}=\frac{15-5}{5-(-1)}=\frac{10}{6}=\frac{5}{3}$

Next, use the slope-intercept form of the equation:

or $15=\frac{5}{3}(5)+b$ where $b=\frac{20}{3}$

So the equation becomes $y=\frac{5}{3}x+ \frac{20}{3}$ or in standard form .

← Didn't Know|Knew It →

Question

What is the length of a line with endpoints at and ?

Tap to reveal answer

Answer

The formula for the length of a line is very similiar to the pythagorean theorem:

Plug in our given numbers to solve:

$\sqrt{25}=\sqrt{l^2}$

← Didn't Know|Knew It →

Question

What is the length of a line with endpoints at and ?

Tap to reveal answer

Answer

The formula for the length of a line is very similiar to the pythagorean theorem:

Plug in our given numbers to solve:

$\sqrt{25}=\sqrt{l^2}$

← Didn't Know|Knew It →

Question

What is the distance between points and ?

Tap to reveal answer

Answer

Use the distance formula:

$d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

Plug in the given points:

$d=\sqrt{(12-(-2)))^2+(3-4)^2}$

$d=\sqrt{197}$

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Question

Find the distance between points and .

Tap to reveal answer

Answer

Use the distance formula:

$d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

Substitute the given points into the formula:

$d=\sqrt{(14-2)^2+(-2-(-4))^2}$

$d=\sqrt{148}$

← Didn't Know|Knew It →

Question

What is the length of a line with endpoints of and ?

Tap to reveal answer

Answer

The distance formula is just a reworking of the Pythagorean theorem: $l=\sqrt{\Delta x^2+\Delta y^2}$

Expand that.

$l=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

Plug in our given values.

$l=\sqrt{(7-2)^2+(9--4)^2}$

$l=\sqrt{(5)^2+(13)^2}$

$l=\sqrt{25+169}$

$l=\sqrt{194}$

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