Question

19. The distance from the origin to the point where the line 5x + 4y = 50 cuts the axis of x is: (A) 9 units (C) 6 units (B) 8 units (D) 10.5 units​.

Anyonee!!!

Answer 1

Given:

Equation of a line, $5x+4y=50$

To find:

Distance from origin to a point where the line cuts x-axis.

Solution:

The equation of line $5x+4y=50$ as plotted on a graph sheet is shown below. This line cuts x-axis at (10,0) as shown in figure. Let this point be A. The distance from origin O(0,0) to A(10,0) is calculated using the distance formula. Let this distance be OA.

$Distance=\sqrt{(x_{2}-x_{1}) ^{2} +(y_{2}-y_{1}) ^{2} }$

Here, $x_{1}=0, y_{1}=0, x_{2}=10, y_{2}=0$

Substituting the values in the formula,

$OA = \sqrt{(10-0)^{2}+(0-0)^{2} }$

$OA=\sqrt{10^{2}+0^{2} }$

$OA=\sqrt{100+0}$

$OA=\sqrt{100}$

$OA =10$ units

The point where a line $5x+4y=50$ cuts at x-axis is (10,0). The distance from origin to this point is 10 units. The correct option is (d).

Answer 2

Answer:

correct answer is (10,0)

but in many books the wrong answer 9 is given