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SSAT Upper Level Math : How to find the length of a line with distance formula

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Example Questions

Example Question #1 : How To Find The Length Of A Line With Distance Formula

A line segment has the endpoints (-1, 3) and (4,-2) . What is the length of this line segment?

Possible Answers:

$5\sqrt2$

$\sqrt{30}$

Correct answer:

$5\sqrt2$

Explanation:

Use the following formula to find the distance between two points:

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

Plug in the points that are given.

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

$\text{Distance}=\sqrt{(5)^2+(-5)^2}$

$\text{Distance}=\sqrt{25+25}=\sqrt{50}=\sqrt{5*5*2}=5\sqrt2$

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Example Question #1 : Distance Formula

A line segment has end points at (8,1) and (-2,-3) . What is the length of this line segment?

Possible Answers:

7.46

9.88

10.77

6.32

Correct answer:

10.77

Explanation:

The distance between two points is given by the following equation:

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

Now, using the two given points, plug them in to find the distance.

$\text{Distance}=\sqrt{(-2-8)^2+(-3-1)^2}=\sqrt{100+16}=\sqrt{116}=10.77$

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Example Question #2 : Distance Formula

Find the length of a line that has end points at $(8, -1)\text{ and }(-2, 1)$ .

Possible Answers:

$2\sqrt{26}$

104

$\sqrt{26}$

126

Correct answer:

$2\sqrt{26}$

Explanation:

Use the distance formula to find the length of this line segment:

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

Substitute in the values provided:

$\text{Distance}=\sqrt{(-2-8)^2+(1-(-1))^2}=\sqrt{100+4}=\sqrt{104}$

At this point, break down the square root:

$\sqrt{104}=\sqrt{2\cdot52}=\sqrt{2\cdot2\cdot26}=\sqrt{2\cdot2\cdot2\cdot13}$

You can remove two of the twos and put them on the outside of the square root symbol, and multiply the two and the thirteen that remain underneath the square root symbol:

$\sqrt{2\cdot2\cdot2\cdot13}=2\sqrt{2\cdot13}=2\sqrt{26}$

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Example Question #3 : How To Find The Length Of A Line With Distance Formula

A line segment has endpoints at $(-2, -1)\text{ and }(8, 1)$ . Find the length of this line.

Possible Answers:

$6\sqrt{3}$

$2\sqrt{26}$

Correct answer:

$2\sqrt{26}$

Explanation:

Use the distance formula to find the length of the line segment.

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

Where,

(x_1,y_1)=(-2,-1) and (x_2,y_2)=(8,1) .

$\text{Distance}=\sqrt{(8-(-2))^2+(1-(-1))^2}=\sqrt{100+4}=\sqrt{104}=2\sqrt{26}$

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Example Question #4 : How To Find The Length Of A Line With Distance Formula

Find the length of the line segment that has endpoints $(0, 4)\text{ and }(12, 6)$ .

Possible Answers:

10.659

12.412

8.451

12.166

Correct answer:

12.166

Explanation:

Use the distance formula to find the length of the line segment.

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

Where,

(x_1,y_1)=(0,4) and (x_2,y_2)=(12,6) .

$\text{Distance}=\sqrt{(12-0)^2+(6-4)^2}=\sqrt{144+4}=\sqrt{148}=12.166$

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Example Question #151 : Geometry

Find the length of the line segment that has the endpoints $(2, 4)\text{ and }(7, 8)$ .

Possible Answers:

$\sqrt{29}$

$\sqrt{31}$

$\sqrt{41}$

Correct answer:

$\sqrt{41}$

Explanation:

Use the distance formula to find the length of the line.

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

Where,

(x_1,y_1)=(2,4) and (x_2,y_2)=(7,8) .

$\text{Distance}=\sqrt{(7-2)^2+(8-4)^2}=\sqrt{25+16}=\sqrt{41}$

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Example Question #1 : How To Find The Length Of A Line With Distance Formula

One leg of a triangle has endpoints at the coordinates $(-1, -2)\text{ and }(-4, -1)$ . Find the length of this leg.

Possible Answers:

$\sqrt{10}$

$2\sqrt2$

Correct answer:

$\sqrt{10}$

Explanation:

Use the distance formula to find the length of the leg.

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

Where,

(x_1,y_1)=(-1,-2) and (x_2,y_2)=(-4,-1) .

$\text{Length}=\sqrt{(-4-(-1))^2+(-1-(-2))^2}=\sqrt{9+1}=\sqrt{10}$

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Example Question #5 : How To Find The Length Of A Line With Distance Formula

A side of a square is graphed onto a coordinate plane. The side has endpoints at $(-3, 1)\text{ and }(4, -1)$ . Find the length of the side of the square.

Possible Answers:

$3\sqrt5$

$\sqrt{53}$

Correct answer:

$\sqrt{53}$

Explanation:

Use the distance formula to find the length of the line segment.

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

Where,

(x_1,y_1)=(-3,1) and (x_2,y_2)=(4,-1)

$\text{Distance}=\sqrt{(4-(-3))^2+(-1-1)^2}=\sqrt{49+4}=\sqrt{53}$

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Example Question #6 : How To Find The Length Of A Line With Distance Formula

The side of a triangle is graphed onto a coordinate plane. The side has endpoints at $(2, 2)\text{ and }(1, -5)$ . Find the length of this side.

Possible Answers:

$5\sqrt2$

$4\sqrt{3}$

Correct answer:

$5\sqrt2$

Explanation:

Use the distance formula to find the length of the line segment.

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

Where,

(x_1,y_1)=(2,2) and (x_2,y_2)=(1, -5) .

$\text{Distance}=\sqrt{(1-2)^2+(-5-2)^2}=\sqrt{1+49}=\sqrt{50}=5\sqrt2$

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Example Question #3 : How To Find The Length Of A Line With Distance Formula

Find the length of a line segment that has endpoints at $(1, 2)\text{ and }(5, 1)$ .

Possible Answers:

$\sqrt{15}$

$\sqrt{17}$

Correct answer:

$\sqrt{17}$

Explanation:

Use the distance formula to find the length of the line segment.

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

Where,

(x_1,y_1)=(1,2) and (x_2,y_2)=(5,1)

$\text{Distance}=\sqrt{(5-1)^2+(1-2)^2}=\sqrt{16+1}=\sqrt{17}$

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SSAT Upper Level Math : How to find the length of a line with distance formula

Study concepts, example questions & explanations for SSAT Upper Level Math

All SSAT Upper Level Math Resources

Example Questions

Example Question #1 : How To Find The Length Of A Line With Distance Formula

Example Question #1 : Distance Formula

Example Question #2 : Distance Formula

Example Question #3 : How To Find The Length Of A Line With Distance Formula

Example Question #4 : How To Find The Length Of A Line With Distance Formula

Example Question #151 : Geometry

Example Question #1 : How To Find The Length Of A Line With Distance Formula

Example Question #5 : How To Find The Length Of A Line With Distance Formula

Example Question #6 : How To Find The Length Of A Line With Distance Formula

Example Question #3 : How To Find The Length Of A Line With Distance Formula

All SSAT Upper Level Math Resources

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