Ask a New Question
Menu

When I tried answering a problem then looked at the answer in the back of my book, I was confused how to get to the correct answer. The problem is there is a trapezoid on a coordinate plane that is centered at the origin. The coordinates of the points have variables: T(-a,0), R(-b,c),A(b,c), P(a,0). The non parallel sides are TR and PA. I have to use the distance formula to find the length of segment TR and segment PA. In the selected answers sections of the book it says the answer is Yes;TR=PA= square root of a^2-2ab+b^2+c^2. How do I get this answer? The answer I got as the square root of a^2+b^2+c^2.

User Icon for Reiny Reiny answered
12 years ago

let's do PA first

PA = √( (a-b)^2 + (0-c)^2 )
= √( a^2 - 2ab + b^2 + c^2 ) , that was easy

now ..
TR = √( (-b + a)^2 + (c-0)^2 )
= √(b^2 - 2ab + a^2 + c^2 )
= PA

I don't see why you didn't get that, all I did was apply the distance formula

I think your problem was in expanding (a-b)^2
= (a-b)(a-b)= a^2 - ab - ab + b^2
= a^2 - 2ab + b^2

User Icon for Explain Bot Explain Bot answered
11 months ago

To find the length of segment TR and segment PA, you need to apply the distance formula. The distance formula calculates the distance between two points in a coordinate plane.

The formula for finding the distance between two points (x1, y1) and (x2, y2) is:

d = √((x2 - x1)^2 + (y2 - y1)^2)

Let's apply this formula to find the length of segment TR:

Point T: T(-a, 0)
Point R: R(-b, c)

Substituting these values into the distance formula:

d(TR) = √((-b - (-a))^2 + (c - 0)^2)
= √((a - b)^2 + c^2)
= √(a^2 - 2ab + b^2 + c^2)

Similarly, for segment PA:

Point P: P(a, 0)
Point A: A(b, c)

d(PA) = √((b - a)^2 + c^2)
= √(a^2 - 2ab + b^2 + c^2)

These two answers, √(a^2 - 2ab + b^2 + c^2), are indeed equal. The book's answer combines the terms a^2, -2ab, and b^2 into a perfect square, (a - b)^2. Therefore, both TR and PA have the same length:

TR = PA = √(a^2 - 2ab + b^2 + c^2)

It seems that you missed the -2ab term when calculating the length. Make sure to double-check your calculations and take all the terms into account to arrive at the correct answer.