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

Short Answer

Expert verified

The distance is 4.

Step by step solution

01

Step-1 – Given

The given points are (3, -4) and (-1, -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,y1beA3,鈭�4andBx2,y2beB鈭�1,鈭�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�1,鈭�4

Then,

AT=x1鈭�x2AT=3鈭�鈭�1AT=3+1AT=4And

BT=y1鈭�y2BT=鈭�4鈭�鈭�4BT=鈭�4+4BT=0

Using the Pythagorean theorem, we get:

AB2=AT2+BT2AB2=42+02AB2=16+0AB2=16AB=4

Hence, the required distance is 4.

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Most popular questions from this chapter

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

(7, 2); (2, 7)

Find the slope and length of AB.

A(3, -1), B(5, -7)

Given points A, B, and C. Find AB, BC, and AC. Are A, B, and C collinear?

If so, which point lies between the other two?

15. A(-5, 6), B(0, 2), C(3, 0)

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(-1, 3) Q(2, 7) R(8, 15)

a. List twelve points, each with integer coordinates, that are 5 units from (-8, 1).

b. Find an equation of the circle containing these points.
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