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Chapter 13: Q. 21 (page 533)

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)

Short Answer

Expert verified

We have proved that the pointsP,QandR are collinear.

Step by step solution

01

Step-1 – Given

The given points areP鈭�8,6,Q鈭�5,5andR4,2.

02

Step-2 – To determine

We have to show that points P,QandRare collinear by showing thatPQ炉 andQR炉 have the same slope.

03

Step-3 – Calculation 

We鈥檒l use the slope formula:

m=y2鈭�y1x2鈭�x1

The given points are P鈭�8,6,Q鈭�5,5andR4,2

Slope ofPQ炉:

y2鈭�y1x2鈭�x1=5鈭�6鈭�5鈭�鈭�8=鈭�13=鈭�0.34

Slope of QR炉:

y2鈭�y1x2鈭�x1=2鈭�54鈭�鈭�5=鈭�39=鈭�0.34

Since, the slope of PQ炉and QR炉are equal, so the pointsP,QandR are collinear.

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Most popular questions from this chapter

In Exercises 27-32 find and then compare lengths of segments.

Quadrilateral TAUL has vertices T(4, 6), A(6, -4), U(~4, -2), and L(-2, 4), Show that the diagonals are congruent.

In Exercises 35-38 find an equation of the circle described and sketch the graph.

The circle has center (p, q) and is tangent to the x-axis.

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?

16. A(3, 4), B(-3, 0), C(-1, 1)

a. Show that tan鈭燗 = slope of AC.

b. Use trigonometry to find m鈭燗.

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)
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