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Chapter 13: Q. 1 (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. (2, -3) and (2, 4)

Short Answer

Expert verified

The distance is 7.

Step by step solution

01

Step-1 – Given

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

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,y1isA鈭�2,鈭�3andBx2,y2isB鈭�2,4

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,鈭�3

Then,

AT=x1鈭�x2AT=鈭�2鈭�鈭�2AT=鈭�2+2AT=0

And

BT=y1鈭�y2BT=鈭�3鈭�4BT=鈭�7BT=鈭�7

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

Using the Pythagorean theorem we get:

AB2=AT2+BT2AB2=02+72AB2=0+49AB2=49AB=7

Hence, the required distance is 7.

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Most popular questions from this chapter

In Exercises 4-9 state:

a. the coordinates of T.

b. the lengths of the legs of the right triangle.

c. the length of the segment shown.

In Exercises 20 and 21 show that points P, Q, and R are collinear by showing that PQ and OR have the same slope.

P(-8, 6) Q(-5, 5) R(4, 2)

A wheelchair ramp is to be built at the town library. If the entrance to the library is 18 in. above ground, and the slope of the ramp is, how far out from the building will the ramp start?

Write an equation of the circle that has the given center and radius.

C(鈭�2,5)鈥夆赌夆赌�;鈥夆赌夆赌�r=13

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)
See all solutions

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