A line of slope 2 passes through the point A(1,3).
a) Check whether B(3,7) is a point on this line.
b) Write down the equation of this line.
c) Find the coordinates of a point C on the line such that BC = 2AB.

Question

Filo · Accepted Answer

Slope of the line is 2 and passes through A(1, 3)

\frac{y - 3}{x - 1} = 2

y - 3 = 2 x - 2

y = 2 x + 1

(a) For point B(3, 7)
2(3) + 1 = 7
Hence the point B(3, 7)lies on the line y = 2x + 1

(b) Equation of the line is y = 2x+1.

(c) Let

(x_{1}, y_{1})

be the coordinates of point C on line.
Therefore it satisfies the equation of line a

y = 2 x + 1

∴ y_{1} = 2 x_{1} + 1

BC = 2 A B

\Rightarrow (x_{1} - 3)^{2} + (y_{1} - 7)^{2} = 2 (3 - 1)^{2} + (7 - 3)^{2}

Squaring both sides, we get

\Rightarrow (x_{1} - 3)^{2} + (y_{1} - 7)^{2} = 4 [(3 - 1)^{2} + (7 - 3)^{2}]

(x_{1} - 3)^{2} + (2 x_{1} + 1 - 7)^{2} = 4 [(2)^{2} + (4)^{2}]

[∴ y_{1} = 2 x_{1} + 1]

5 (x_{1} - 3)^{2} = 80

(x_{1} - 3)^{2} = 16

x_{1} - 3 = \pm 4

x_{1} = 7

or

- 1

y_{1} = 2 x_{1} + 1 = 2 (7) + 1 = 15

y_{1} = 2 x_{1} + 1 = 2 (- 1) + 1 = - 1

The coordinates of point C are

(7, 15)

or

(- 1, - 1)

.

Question Text	A line of slope 2 passes through the point A(1,3). a) Check whether B(3,7) is a point on this line. b) Write down the equation of this line. c) Find the coordinates of a point C on the line such that BC = 2AB.
Answer Type	Text solution:1
Upvotes	150

A line of slope 2 passes through the point A(1,3).
a) Check whether B(3,7) is a point on this line.
b) Write down the equation of this line.
c) Find the coordinates of a point C on the line such that BC = 2AB.

Text solutionVerified

Practice questions from similar books

A line of slope 2 passes through the point A(1,3).a) Check whether B(3,7) is a point on this line.b) Write down the equation of this line.c) Find the coordinates of a point C on the line such that BC = 2AB.

Text solutionVerified

Practice questions from similar books

A line of slope 2 passes through the point A(1,3).
a) Check whether B(3,7) is a point on this line.
b) Write down the equation of this line.
c) Find the coordinates of a point C on the line such that BC = 2AB.