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Chapter 13: Q. 2 (page 526)

Find the distance between the two points. If necessary, you may draw graphs but you shouldn鈥檛 need to use the distance formula.

  1. (3, 3) and (-2, 3)

Short Answer

Expert verified

The distance is 5.

Step by step solution

01

Step-1 – Given

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

02

Step-2 – To determine

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

03

Step-3 – Calculation 

Let, the coordinate ofAx1,y1isA3,3andBx2,y2isB鈭�2,3

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

So, the coordinate of Tisx2,y1=鈭�2,3

Then,

AT=x1鈭�x2AT=3鈭�鈭�2AT=3+2AT=5

And

BT=y1鈭�y2BT=3鈭�3BT=0

Using the Pythagorean theorem, we get:

AB2=AT2+BT2AB2=52+02AB2=25+0AB2=25AB=5

Hence, the required distance is 5.

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Find the slope of the line through the points named. If the slope is not defined, write not defined.

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