Question

If the slope of the line passing through the point $A(3,2)$ is $\frac{3}{4}$,then the point on the line $5$ units away from $A$is.

• A. $(-1.-1)$
• B. $(7,5)$
• C. $(7,-5)$
• D. Both A and B

Answer 1

The correct option is D

Both A and B

Explanation for correct option:

Option (A):

If the slope of the line passing through the point $A(3,2)$ is $\frac{3}{4}$,Then

Considering the point as $(-1.-1)$ , the length is given as

$l=\sqrt{{(x_2-x_1)}^2+{(y_2-y_1)}^2}$

$\Rightarrow l=\sqrt{{(3+1)}^2+{(2+1)}^2}$

$\Rightarrow l=\sqrt{3^2+4^2}$

$\Rightarrow l=5$

Option (B):

If the slope of the line passing through the point $A(3,2)$ is $\frac{3}{4}$,Then

Considering $(7,5)$ length is given as

$l=\sqrt{{(x_2-x_1)}^2+{(y_2-y_1)}^2}$

$\Rightarrow l=\sqrt{{(3-7)}^2+{(2-5)}^2}$

$\Rightarrow l=\sqrt{{(-4)}^2+{(-3)}^2}$

$\Rightarrow l=5$

Explanation for incorrect options :

Option (C):

If the slope of the line passing through the point $A(3,2)$ is $\frac{3}{4}$,Then

Considering option ( C) $(7,-5)$, length is given as

$l=\sqrt{{(x_2-x_1)}^2+{(y_2-y_1)}^2}$

$\Rightarrow l=\sqrt{{(3-7)}^2+{(2+5)}^2}$

$\Rightarrow l=\sqrt{{(-4)}^2+{\left(7\right)}^2}$

$\Rightarrow l=\sqrt{65}\ne 5$

Therefore, option (A) and (B) are correct