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Algebra 1 : Functions and Lines

Study concepts, example questions & explanations for Algebra 1

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10 Diagnostic Tests 557 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #36 : How To Find The Length Of A Line With Distance Formula

Find the distance between the following points:

(14,25)(38,7)

Possible Answers:

Correct answer:

Explanation:

Find the distance between the following points:

(14,25)(38,7)

To find the distance between two points, use distance formula.

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

Distance formula is closely related to Pythagorean theorem. Pythagorean Theorem is:

a^2+b^2=c^2

Which can be rewritten as:

$c=\sqrt{a^2+b^2}$

Now, in distance formula, we are essentially finding the hypotenuse of a right triangle.

Anyway, to find the distance, we simply need to plug in the points we are given and simplify:

$d=\sqrt{(38-14)^2+(7-25)^2}=\sqrt{(24^2)+(-18)^2}$

Continue

$\sqrt{(24^2)+(-18)^2}=\sqrt{576+324}=\sqrt{900}=30$

So our hypotenuse (distance) is 30.

If you are really observant, you can see that the other two sides of the triangles are 24 and 18.

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Example Question #37 : How To Find The Length Of A Line With Distance Formula

A line is connected by the points (1,3) and (4,2) . What is the distance of this line?

Possible Answers:

$2\sqrt3$

$\sqrt{10}$

$2\sqrt5$

$2\sqrt2$

Correct answer:

$\sqrt{10}$

Explanation:

Write the distance formula.

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

Substitute the values of the points inside the equation.

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

Simplify by order of operations.

$d= \sqrt{(3)^2+(-1)^2} = \sqrt{9+1} = \sqrt{10}$

The length of the line is $\sqrt{10}$ .

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Example Question #31 : How To Find The Length Of A Line With Distance Formula

Find the distance between these two points using the distance formula:

(2, 6) and (-4, 8)

Possible Answers:

$\sqrt{40}$

$\sqrt{6}$

$\sqrt{10}$

Correct answer:

$\sqrt{40}$

Explanation:

To find the distance between two points using the distance formula, we use the following formula:

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

where (x_1, y_1) and (x_2, y_2) are the given points. So, we can substitute the points (2, 6) and (-4, 8) .

$d = \sqrt{(-4 - 2)^2 + (8 - 6)^2}$

$d = \sqrt{(-6)^2 + (2)^2}$

$d = \sqrt{36 + 4}$

$d = \sqrt{40}$

Therefore, the distance is $\sqrt{40}$ .

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Example Question #41 : Points And Distance Formula

Find the length of the line with endpoints (-7, 2) and (5, 9) using the distance formula.

Possible Answers:

$\sqrt{193}$

$\sqrt{125}$

$\sqrt{19}$

193

Correct answer:

$\sqrt{193}$

Explanation:

To solve, we will use the distance formula:

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

where (x_1, y_1) and (x_2, y_2) are the given points. Given the points

(-7, 2) and (5, 9)

we can substitute into the formula. We get,

$\text{distance} = \sqrt{(5 - - 7)^2 + (9 - 2)^2}$

$\text{distance} = \sqrt{(12)^2 + (7)^2}$

$\text{distance} = \sqrt{144 + 49}$

$\text{distance} = \sqrt{193}$

Therefore, the length of the line with the endpoints (-7, 2) and (5, 9) is $\sqrt{193}$ .

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Example Question #42 : How To Find The Length Of A Line With Distance Formula

Given the following two points:

(8,7) (1,5)

Calculate the distance between the two points using the distance formula. Round your answer to one decimal place.

Possible Answers:

7.9

8.4

6.8

7.3

10.1

Correct answer:

7.3

Explanation:

The distance formula equation is as follows:

$d = \sqrt{(x1-x2)^{2} + (y1-y2)^{2}}$

Note that x1,x2,y1, y2 simply refer to the 'first and ' and 'second and ' points, these are simply for keeping track and do not require any further computation.

The and coordinates given can be plugged in to solve for the distance between these two points.

$d = \sqrt{(8-1)^{2} + (7-5)^{2}}$

$d = \sqrt{(7)^{2} + (2)^{2}}$

$d = \sqrt{49 + 4}$

$d = \sqrt{53}$

d = 7.3

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Example Question #3911 : Algebra 1

Find the length of the line with the endpoints (0, 5) and (6, 8).

Possible Answers:

$\sqrt{28}$

$\sqrt{205}$

$\sqrt{45}$

$\sqrt{19}$

$\sqrt{-9}$

Correct answer:

$\sqrt{45}$

Explanation:

To find the length of a line, we use the distance formula

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

where (x_1, y_1) and (x_2, y_2) are the endpoints. Knowing this, we can substitute the endpoints into the equation. We get

$\sqrt{(6-0)^2 + (8-5)^2}$

$\sqrt{6^2 + 3^2}$

$\sqrt{36 + 9}$

$\sqrt{45}$

Therefore, the length of the line with the endpoints (0, 5) and (6, 8) is $\sqrt{45}$ .

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Example Question #41 : How To Find The Length Of A Line With Distance Formula

Find the length of the line with the following endpoints:

(12,1)(6,4)

Possible Answers:

$3\sqrt{5}$

$\sqrt{47}$

$\sqrt{46}$

$2\sqrt{11}$

Correct answer:

$3\sqrt{5}$

Explanation:

In order to find the distance between two points on a line, use the formula below:

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

Plug in the points (12,1) and (6,4) and solve:

$\sqrt{(12-6)^{2}+(1-4)^{2}}=\sqrt{(6)^{2}+(-3)^{2}}=\sqrt{36+9}=\sqrt{45}=3\sqrt{5}$

This gives a final answer of $3\sqrt{5}$

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Example Question #41 : How To Find The Length Of A Line With Distance Formula

Find the length of the line with the following endpoints:

(15,5)(3,5)

Possible Answers:

$10\sqrt{2}$

$\sqrt{147}$

Correct answer:

Explanation:

In order to find the distance between two points on a line, use the formula below:

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

Plug in the points (15,5) and (3,5) and solve:

$\sqrt{(15-3)^{2}+(5-5)^{2}}=\sqrt{(12)^{2}+(0)^{2}}=\sqrt{144}=12$

This gives a final answer of

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Example Question #46 : Points And Distance Formula

Find the length of the line with the following endpoints:

(-6,-12)(2,7)

Possible Answers:

$5\sqrt{17}$

$\sqrt{427}$

$\sqrt{471}$

$2\sqrt{105}$

Correct answer:

$5\sqrt{17}$

Explanation:

In order to find the distance between two points on a line, use the formula below:

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

Plug in the points (-6,-12) and (2,7) and solve:

$\sqrt{(7+12)^{2}+(2+6)^{2}}=\sqrt{(19)^{2}+(8)^{2}}=\sqrt{361+64}=\sqrt{425}=5\sqrt{17}$

This gives a final answer of $5\sqrt{17}$

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Example Question #42 : Points And Distance Formula

Find the length of the line with the following endpoints:

(9,4)(-6,2)

Possible Answers:

$\sqrt{229}$

$\sqrt{227}$

$\sqrt{231}$

$7\sqrt{5}$

Correct answer:

$\sqrt{229}$

Explanation:

In order to find the distance between two points on a line, use the formula below:

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

Plug in the points (9,4) and (-6,2) and solve:

$\sqrt{(9+6)^{2}+(4-2)^{2}}=\sqrt{(15)^{2}+(2)^{2}}=\sqrt{225+4}=\sqrt{229}$

This gives a final answer of $\sqrt{229}$

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Algebra 1 : Functions and Lines

Study concepts, example questions & explanations for Algebra 1

All Algebra 1 Resources

Example Questions

Example Question #36 : How To Find The Length Of A Line With Distance Formula

Example Question #37 : How To Find The Length Of A Line With Distance Formula

Example Question #31 : How To Find The Length Of A Line With Distance Formula

Example Question #41 : Points And Distance Formula

Example Question #42 : How To Find The Length Of A Line With Distance Formula

Example Question #3911 : Algebra 1

Example Question #41 : How To Find The Length Of A Line With Distance Formula

Example Question #41 : How To Find The Length Of A Line With Distance Formula

Example Question #46 : Points And Distance Formula

Example Question #42 : Points And Distance Formula

All Algebra 1 Resources

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