Chapter 13: Q. 1 (page 526)

Find the distance between the two points. If necessary, you may draw graphs but you shouldn’t need to use the distance formula.
(2, -3) and (2, 4)

Short Answer

Expert verified

The distance is 7.

Step by step solution

Step-1 – Given

The given points are (-2, -3) and (-2, 4).

Step-2 – To determine

We have to find the distance between the two points without using distance formula.

Step-3 – Calculation

Let, the coordinate of $A (x_{1}, y_{1}) is A (- 2, - 3) and B (x_{2}, y_{2}) is B (- 2, 4)$

Let T be the point where the horizontal line through A and vertical line through B meets.

So, the coordinate of Tis $(x_{2}, y_{1}) = (- 2, - 3)$

Then,

$\begin{array}{l} A T = (x_{1} - x_{2}) \\ A T = (- 2 - (- 2)) \\ A T = (- 2 + 2) \\ A T = 0 \end{array}$

And

$\begin{array}{l} B T = (y_{1} - y_{2}) \\ B T = (- 3 - 4) \\ B T = (- 7) \\ B T = - 7 \end{array}$

BT is a distance and distancecannot be negative. Therefore, BT = 7.

Using the Pythagorean theorem we get:

$\begin{array}{l} {(A B)}^{2} = {(A T)}^{2} + {(B T)}^{2} \\ {(A B)}^{2} = {(0)}^{2} + {(7)}^{2} \\ {(A B)}^{2} = 0 + 49 \\ {(A B)}^{2} = 49 \\ A B = 7 \end{array}$

Hence, the required distance is 7.

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Find the distance between the two points. If necessary, you may draw graphs but you shouldn’t need to use the distance formula.
(2, -3) and (2, 4)

Short Answer

Step by step solution

Step-1 – Given

Step-2 – To determine

Step-3 – Calculation

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Find the distance between the two points. If necessary, you may draw graphs but you shouldn’t need to use the distance formula.(2, -3) and (2, 4)

Short Answer

Step by step solution

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

Mechanics Maths

Logic and Functions

Discrete Mathematics

Probability and Statistics

Decision Maths

Applied Mathematics

Study anywhere. Anytime. Across all devices.

Find the distance between the two points. If necessary, you may draw graphs but you shouldn’t need to use the distance formula.
(2, -3) and (2, 4)