Q58. Find the possible values for聽if... [FREE SOLUTION]

91影视

Algebra 1

Carter, Cuevas, Day, Holiday, Luchin

$Math Studyset 91影视 Explanations$ Math

Student Edition 路 801 pages

ISBN: 9780078884801

Chapter 10: Q58. (page 659)

Find the possible values forif the points with the given coordinates are the indicated distance apart.
$(1, a)$ , $(鈭� 3, 2)$ ; $d = 5$

Short Answer

Expert verified

The possible values for a are5 and $- 1$ .

Step by step solution

Step 1. Given.

Given data is $(1, a), (鈭� 3, 2); d = 5 (1, a), (鈭� 3, 2); d = 5$

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:

width="191">d=x2鈭�x12+y2鈭�y12

Step 3. Find the possible values for a.

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

It is also given that the distance between the given points is 5. Therefore, the value d is 5.

Therefore, it is obtained that:

$d = \sqrt{{(x_{2} 鈭� x_{1})}^{2} + {(y_{2} 鈭� y_{1})}^{2}} 5 = \sqrt{{(鈭� 3 鈭� 1)}^{2} + {(2 鈭� a)}^{2}} 5 = \sqrt{{(鈭� 4)}^{2} + {(2 鈭� a)}^{2}} 5 = \sqrt{16 + 2^{2} 鈭� 2 (2) (a) + a^{2}} (鈭� {(a 鈭� b)}^{2} = a^{2} 鈭� 2 a b + b^{2}) 5 = \sqrt{a^{2} 鈭� 4 a + 20} {(5)}^{2} = {(\sqrt{a^{2} 鈭� 4 a + 20})}^{2} 25 = a^{2} 鈭� 4 a + 20 0 = a^{2} 鈭� 4 a + 20 鈭� 25 0 = a^{2} 鈭� 4 a 鈭� 5 0 = a^{2} 鈭� 5 a + a 鈭� 5 0 = a (a 鈭� 5) + 1 (a 鈭� 5) 0 = (a 鈭� 5) (a + 1) a 鈭� 5 = 0 or a + 1 = 0 a = 5 or a = 鈭� 1$

Therefore, the possible values for a are 5 and $- 1$ .

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91影视

Find the possible values forif the points with the given coordinates are the indicated distance apart.
$(1, a)$ , $(鈭� 3, 2)$ ; $d = 5$

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.

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91影视

Find the possible values forif the points with the given coordinates are the indicated distance apart.1,a, 鈭�3,2;d=5

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

Mechanics Maths

Pure Maths

Theoretical and Mathematical Physics

Decision Maths

Calculus

Geometry

Study anywhere. Anytime. Across all devices.

Find the possible values forif the points with the given coordinates are the indicated distance apart.
$(1, a)$ , $(鈭� 3, 2)$ ; $d = 5$