Chapter 13: Q. 10CE (page 526)

10. Find the distance between the points named. Give all answers in simplest
form.
(0, 0) and (5, -3).
(3, -2) and (-5, -2).
3. (4, 4) and (-3, -3).

Short Answer

Expert verified

The distance is $\sqrt{34}$ .
The distance is 8.
The distance is $\sqrt{98}$

Step by step solution

a.Step-1 – Given

The given points are (0,0) and (5, -3).

Step-2 – To determine

We have to find the distance between the points.

Step-3 – Calculation

We will use the distance formula.

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

with $x_{1} = 0, x_{2} = 5, y_{1} = 0 and y_{2} = - 3$

$\begin{array}{l} d = \sqrt{{(5 - 0)}^{2} + {(- 3 - 0)}^{2}} [d = distance] \\ d = \sqrt{{(5)}^{2} + {(- 3)}^{2}} \\ d = \sqrt{25 + 9} \\ d = \sqrt{34} \end{array}$

So, the distance is $\sqrt{34}$ .

b.Step-1 – Given

The given points are (3, -2) and (-5, -2).

Step-2 – To determine

We have to find the distance between the points.

Step-3 – Calculation

We will use the distance formula.

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

With $x_{1} = 3, x_{2} = - 5, y_{1} = - 2 and y_{2} = - 2$

$\begin{array}{l} d = \sqrt{{(- 5 - 3)}^{2} + {(- 2 - (- 2))}^{2}} [d = distance] \\ d = \sqrt{{(- 8)}^{2} + {(- 2 + 2)}^{2}} \\ d = \sqrt{{(- 8)}^{2} + {(0)}^{2}} \\ d = \sqrt{64 + 0} \\ d = \sqrt{64} \\ d = 8 \end{array}$

So, the distance is 8.

c.Step-1 – Given

The given points are (4, 4) and (-3, -3).

Step-2 – To determine

We have to find the distance between the points.

Step-3 – Calculation

We will use the distance formula.

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

with $x_{1} = 4, x_{2} = - 3, y_{1} = 4 and y_{2} = - 3$

$\begin{array}{l} d = \sqrt{{(- 3 - 4)}^{2} + {(- 3 - 4)}^{2}} [d = distance] \\ d = \sqrt{{(- 7)}^{2} + {(- 7)}^{2}} \\ d = \sqrt{49 + 49} \\ d = \sqrt{98} \end{array}$

So, the distance is $\sqrt{98}$ .

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10. Find the distance between the points named. Give all answers in simplest
form.
(0, 0) and (5, -3).
(3, -2) and (-5, -2).
3. (4, 4) and (-3, -3).

Short Answer

Step by step solution

a.Step-1 – Given

Step-2 – To determine

Step-3 – Calculation

b.Step-1 – Given

Step-2 – To determine

Step-3 – Calculation

c.Step-1 – Given

Step-2 – To determine

Step-3 – Calculation

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10. Find the distance between the points named. Give all answers in simplestform.(0, 0) and (5, -3).(3, -2) and (-5, -2). 3. (4, 4) and (-3, -3).

Short Answer

Step by step solution

a.Step-1 – Given

Step-2 – To determine

Step-3 – Calculation

b.Step-1 – Given

Step-2 – To determine

Step-3 – Calculation

c.Step-1 – Given

Step-2 – To determine

Step-3 – Calculation

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Probability and Statistics

Statistics

Discrete Mathematics

Theoretical and Mathematical Physics

Pure Maths

Mechanics Maths

Study anywhere. Anytime. Across all devices.

10. Find the distance between the points named. Give all answers in simplest
form.
(0, 0) and (5, -3).
(3, -2) and (-5, -2).
3. (4, 4) and (-3, -3).