   Chapter 0.7, Problem 18E

Chapter
Section
Textbook Problem

Find the value of k such that ( k , k ) is equidistant from ( − 1 , 0 ) and ( 0 , 2 ) .

To determine

To calculate: The value of k such that (k,k) is equidistant from (1,0) and (0,2).

Explanation

Given Information:

The provided points are (k,k), (1,0) and (0,2).

Formula used:

Distance formula:

Let d be the distance between two points (x1,y1) and (x2,y2) then

d=(x2x1)2+(y2y1)2

Where, x1, y1, x2, and y2 are co-ordinates.

Calculation:

Consider the points (k,k) and (1,0), (0,2)

Point (k,k) is equidistant from point (1,0) and (0,2).

Apply the distance formula,

(k(1))2+(k0)2=(k0)2+(k2)2(k+1)2+k2=k2+(k2)2

Square both sides in the above equation,

(k+1)2+k2=k2+

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