Q57. Find the possible values for a聽... [FREE SOLUTION]

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Algebra 1

Carter, Cuevas, Day, Holiday, Luchin

$Math Studyset 91影视 Explanations$ Math

Student Edition 路 801 pages

ISBN: 9780078884801

Chapter 10: Q57. (page 659)

Find the possible values for aif the points with the given coordinates are the indicated distance apart.
$(5, 鈭� 2)$ , $(a, 鈭� 3)$ ; $d = \sqrt{170}$

Short Answer

Expert verified

The possible values for a are 18 and $- 8$ .

Step by step solution

Step 1. Given.

Coordinates are $(5, 鈭� 2), (a, 鈭� 3); d = \sqrt{170}$

Step 2. Write the distance formula to find the distance between the given two points.

The distance (d) between the points $(x_{1}, y_{1})$ and $(x_{2}, y_{2})$ is given by:

$d = \sqrt{{(x_{2} 鈭� x_{1})}^{2} + {(y_{2} 鈭� y_{1})}^{2}}$

Step 3. Find the possible values for a.

It is given that the two points are $(5, 鈭� 2)$ and $(a, 鈭� 3)$ . Therefore, the values of $x_{1}$ , , $y_{1}$ $x_{2}$ and $y_{2}$ are 5, $鈭� 2$ , a and $- 3$ respectively.

It is also given that the distance between the given points is $\sqrt{170}$ . Therefore, the value of d is $\sqrt{170}$ .

Therefore, it is obtained that:

$d = \sqrt{{(x_{2} 鈭� x_{1})}^{2} + {(y_{2} 鈭� y_{1})}^{2}} \sqrt{170} = \sqrt{{(a 鈭� 5)}^{2} + {(鈭� 3 鈭� (鈭� 2))}^{2}} \sqrt{170} = \sqrt{{(a 鈭� 5)}^{2} + {(鈭� 3 + 2)}^{2}} \sqrt{170} = \sqrt{a^{2} 鈭� 2 (a) (5) + 5^{2} + {(鈭� 1)}^{2}} (鈭� {(a 鈭� b)}^{2} = a^{2} 鈭� 2 a b + b^{2}) \sqrt{170} = \sqrt{a^{2} 鈭� 10 a + 26} {(\sqrt{170})}^{2} = {(\sqrt{a^{2} 鈭� 10 a + 26})}^{2} 170 = a^{2} 鈭� 10 a + 26 0 = a^{2} 鈭� 10 a + 26 鈭� 170 0 = a^{2} 鈭� 10 a 鈭� 144 0 = a^{2} 鈭� 18 a + 8 a 鈭� 144 0 = a (a 鈭� 18) + 8 (a 鈭� 18) 0 = (a 鈭� 18) (a + 8) a 鈭� 18 = 0 or a + 8 = 0 a = 18 or a = 鈭� 8$

Therefore, the possible values for a are 18 and $- 8$ .

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91影视

Find the possible values for aif the points with the given coordinates are the indicated distance apart.
$(5, 鈭� 2)$ , $(a, 鈭� 3)$ ; $d = \sqrt{170}$

Short Answer

Step by step solution

Step 1. Given.

Step 2. Write the distance formula to find the distance between the given two points.

Step 3. Find the possible values for a.

One App. One Place for Learning.

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91影视

Find the possible values for aif the points with the given coordinates are the indicated distance apart.5,鈭�2, a,鈭�3;d=170

Short Answer

Step by step solution

Step 1. Given.

Step 2. Write the distance formula to find the distance between the given two points.

Step 3. Find the possible values for a.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Probability and Statistics

Geometry

Pure Maths

Decision Maths

Statistics

Discrete Mathematics

Study anywhere. Anytime. Across all devices.

Find the possible values for aif the points with the given coordinates are the indicated distance apart.
$(5, 鈭� 2)$ , $(a, 鈭� 3)$ ; $d = \sqrt{170}$