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Chapter 13: Q34. (page 534)

Find two values of k such that the points (-3, 4), (0, k), and (k, 10) are collinear.

Short Answer

Expert verified

The two values of k are−5,6 .

Step by step solution

01

Step-1 – Given

The given points are(−3,4),(0,k)and(k,10) .

02

Step-2 – To determine

We have tofind two values ofk such that the points(−3,4),(0,k)and(k,10) are collinear.

03

Step-3 – Calculation 

The slope formula for two points(x1,y1)  and  (x2,y2) is:m=y2−y1x2−x1 .

The given points areA(−3,4),B(0,k)andC(k,10).

Since the given points are collinear so:

mAB=mBC=mACk−40−(−3)=10−kk−0=10−4k−(−3)

Solving this equation, we get:

mAB=mBCk−40−(−3)=10−kk−0k−43=10−kkk(k−4)=3(10−k)k2−4k=30−3kk2−k−30=0k2−6k+5k−30=0k(k−6)+5(k−6)=0(k−6)(k+5)=0k−6=0k=6k+5=0k=−5

So, the two values of k are −5,6.

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Most popular questions from this chapter

Discover and prove something about the quadrilateral with vertices

R(-1, -6), A(1, -3), Y(11, 1), and J(9, -2)

Find the slope of the line.

a. Show that tan∠A = slope of AC.

b. Use trigonometry to find m∠A.

There are twelve points, each with integer coordinates, that are 10 units from the origin. List the points. (Hint: Recall the 6, 8, 10 right triangle.)

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

Show that the triangle with vertices D(0, 0), E(3, 1), and F(-2, 6) is a right triangle, then find the area of the triangle.
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