Chapter 10: Q58. (page 659)

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

Short Answer

Expert verified

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

Step by step solution

Step 1. Given.

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

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−x12+y2−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:

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

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

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

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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Find the possible values forif the points with the given coordinates are the indicated distance apart.1,a, −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

Theoretical and Mathematical Physics

Pure Maths

Logic and Functions

Calculus

Geometry

Applied Mathematics

Study anywhere. Anytime. Across all devices.

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