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Chapter 13: Q33. (page 534)

A ine through H(3, 1) and J(5, a) has positive slope and makes a 60° angle measured counterclockwise with the positive x-axis. Find the value of a.

Short Answer

Expert verified

The value of a is23+1 .

Step by step solution

01

Step-1 – Given

Given that: A line through points H(3,1)and J(5,a)has positive slope and makes a60° angle measured counterclockwise with the positivex−axis .

02

Step-2 – To determine

We have tofind the value ofa.

03

Step-3 – Calculation 

The slope formula with two points(x1,y1)and(x2,y2)is

m=y2−y1x2−x1

The given points areH(3,1)and J(5,a).

We know that, the slope of a line is defined as “the tangent of the angle which the line makes with positive direction of thex−axisin the anticlockwise direction”.

It meansm=tanθ

So,

tanθ=y2−y1x2−x1tan60∘=a−15−33=a−12a=23+1

Hence, the value of a is23+1 .

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Most popular questions from this chapter

Find the distance between the two points. If necessary, you may draw graphs but you shouldn’t need to use the distance formula.

  1. (3, 3) and (-2, 3)

Find the slope and length of AB.

A(3, -1), B(5, -7)

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?

14. A(5, -5), B(0, 5), C(2, 1)

In Exercises 4-9 state:

a. the coordinates of T.

b. the lengths of the legs of the right triangle.

c. the length of the segment shown.

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)
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