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SSAT Upper Level Math : Coordinate Geometry

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Example Questions

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 #151 : Geometry

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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Example Question #101 : Coordinate Geometry

Find the length of a line segment that has endpoints at $\left(\frac{5}{2}, \frac{5}{2}\right)$ and $\left(4, \frac{4}{5}\right)$ .

Possible Answers:

4.19

2.27

5.14

3.78

Correct answer:

2.27

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,

$(x_1,y_1)=\left(\frac{5}{2}, \frac{5}{2} \right )$ and $(x_2,y_2)=\left(4,\frac{4}{5} \right )$ .

$\text{Distance}=\sqrt{(4-\frac{5}{2})^2+(\frac{4}{5}-\frac{5}{2})^2}=\sqrt{\frac{9}{4}+\frac{289}{100}}=2.27$

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Example Question #102 : Coordinate Geometry

Find the distance of a line segment that has endpoints at $\left(\frac{1}{2}, 4\right)$ and $\left(\frac{3}{2}, 2\right)$ .

Possible Answers:

$\sqrt3$

$\sqrt5$

Correct answer:

$\sqrt5$

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,

$(x_1,y_1)=\left(\frac{1}{2}, 4 \right )$ and $(x_2,y_2)=\left(\frac{3}{2}, 2 \right )$ .

$\text{Distance}=\sqrt{(\frac{3}{2}-\frac{1}{2})^2+(2-4)^2}=\sqrt{1+4}=\sqrt{5}$

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Example Question #103 : Coordinate Geometry

Find the length of a line segment that has endpoints at $\left(\frac{1}{3}, 2\right)$ and $\left(\frac{4}{3}, 3\right)$ .

Possible Answers:

$2\sqrt2$

$\sqrt2$

Correct answer:

$\sqrt2$

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,

$(x_1,y_1)=\left(\frac{1}{3}, 2\right)$ and $(x_2,y_2)=\left(\frac{4}{3}, 3 \right )$ .

$\text{Distance}=\sqrt{(\frac{4}{3}-\frac{1}{3})^2+(3-2)^2}=\sqrt{1+1}=\sqrt2$

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Example Question #384 : Ssat Upper Level Quantitative (Math)

Find the length of a line segment that has endpoints at $(2, 1)\text{ and }(-1, 0)$ .

Possible Answers:

$2\sqrt2$

$\sqrt{10}$

Correct answer:

$\sqrt{10}$

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)=(2,1) and (x_2,y_2)=(-1,0) .

$\text{Distance}=\sqrt{(-1-2)^2+(0-1)^2}=\sqrt{9+1}=\sqrt{10}$

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Example Question #385 : Ssat Upper Level Quantitative (Math)

Find the length of a line segment that has endpoints at $(3, 1)\text{ and }(-2, -2)$ .

Possible Answers:

$4\sqrt3$

$\sqrt{34}$

Correct answer:

$\sqrt{34}$

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)=(-2,-2) .

$\text{Distance}=\sqrt{(-2-3)^2+(-2-1)^2}=\sqrt{25+9}=\sqrt{34}$

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Example Question #104 : Coordinate Geometry

If the two points on a line are $“\left(“\frac{1}{3}, \frac{1}{3}“\right)”$ and (2,4) , what is the approximate distance connecting the two points?

Possible Answers:

3.7

4.5

4.2

3.5

Correct answer:

Explanation:

Write the distance formula.

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

Substitute the point values.

$d=\sqrt{\left( 4-\frac{1}{3}\right)^2+\left( 2-\frac{1}{3}\right)^2} = \sqrt{\left( \frac{11}{3}\right)^2+\left( \frac{5}{3}\right)^2}$

$d=\sqrt{13.\bar{4}+2.\bar{7}}= \sqrt{16.\bar{2}}= 4.027$

The approximated distance is 4.

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Example Question #105 : Coordinate Geometry

A segment on the coordinate plane whose endpoints are (A, A) and the origin has length 10. Calculate .

Possible Answers:

$A = \pm 5 \sqrt{3}$

$A = \pm 10 \sqrt{2}$

$A = \pm 5$

$A = \pm 5 \sqrt{2}$

$A = \pm 10$

Correct answer:

$A = \pm 5 \sqrt{2}$

Explanation:

The distance between two points $(x_{1}, x_{2})$ and $(y_{1}, y_{2})$ can be obtained using the formula

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

If we set $x_{1}= y_{1} = 0, x_{2}= y_{2} = A, d=10$ , we can solve for :

$10= \sqrt{\left (A-0 \right )^{2}+\left (A-0 \right )^{2}}$

$10= \sqrt{ A ^{2}+A ^{2}}$

$10= \sqrt{ 2A ^{2}}$

$10^{2}=\left ( \sqrt{ 2A ^{2}} \right )^{2}$

$100 = 2A^{2 }$

$100 \div 2 = 2A^{2 } \div 2$

$50 = A^{2}$

$A = \pm \sqrt{50 } = \pm \sqrt{25} \cdot \sqrt{2} = \pm 5 \sqrt{2}$

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SSAT Upper Level Math : Coordinate Geometry

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

All SSAT Upper Level Math Resources

Example Questions

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 #151 : Geometry

Example Question #101 : Coordinate Geometry

Example Question #102 : Coordinate Geometry

Example Question #103 : Coordinate Geometry

Example Question #384 : Ssat Upper Level Quantitative (Math)

Example Question #385 : Ssat Upper Level Quantitative (Math)

Example Question #104 : Coordinate Geometry

Example Question #105 : Coordinate Geometry

All SSAT Upper Level Math Resources

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