SOLUTION: Q.3: Given A(-1,4) and B (5,2),find
(a) the point P on the x-axis such that AP=BP.
(b) the point Q on the y-axis such that AQ=BQ
Algebra.Com
Question 214198: Q.3: Given A(-1,4) and B (5,2),find
(a) the point P on the x-axis such that AP=BP.
(b) the point Q on the y-axis such that AQ=BQ
Answer by drj(1380) (Show Source): You can put this solution on YOUR website!
Q.3: Given A(-1,4) and B (5,2),find
(a) the point P on the x-axis such that AP=BP.
(b) the point Q on the y-axis such that AQ=BQ
Step 1. For part 3(a), the point on the x-axis is y=0 for the coordinates. Let x be coordinate on the x-axis. Point P is (x,0). Then left side of the equation given below is the distance between points A(-1,4) and P(x,0) and the right side is the distances between B(5,2) and P(x,0).
Squaring both sides yields:
Add 10x-17 to both sides of the equation
Divide by 12 yields,
ANSWER: So our point is (1,0).
Step 2. For part 3(b), the point on the y-axis is x=0 for the coordinates. Let x be coordinate on the x-axis. Point Q is (0,y). The left side of the equation below the is distance between Q(0,y) and A(-1,4). The right side is the distance between Q(0,y) and B(5,2)
Squaring both sides yields:
Add 8y-29 to both sides of the equation
Divide by 4 to both sides of the equation
ANSWER So our point is (0,-3).
I hope the above steps were helpful.
For free Step-By-Step Videos on Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra or for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry.
And good luck in your studies!
Respectfully,
Dr J
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