Question

if a slope of the line passing through the point A(3,2) then find the point on the line 5,units away from the point A​

Answer 1

Answer:

Step-by-step explanation:

Answer 2

Question:

If the slope of a line passing through the point A(3, 2) be $\frac{3}{4}$ then the points on the line which are 5 units away from A are

$A. \quad(5,5),(-1,-1)$

$B. \quad(7,5),(-1,-1)$

$C. \quad(5,7),(-1,-1)$

$D. \quad(7,5),(1,1)$

Answer:

Option B: $(7,5),(-1,-1)$ are the coordinates that are 5 units away from point A.

Explanation:

It is given that the slope is $m=\frac{3}{4}$

The slope passes through the point $A(3,2)$

The formula for equation of the line is given by

$y-y_1=m(x-x_1)$

 $y-2=\frac{3}{4} (x-3)$

 $y-2=\frac{3}{4} x-\frac{9}{4}$

       $y=\left\frac{3}{4}\right x-\frac{1}{4}$

Thus, the ordered pair from the equation of line is given by $(x,\frac{3}{4} x-\frac{1}{4})$

To determine the coordinates that are 5 units away from point A using the distance formula,

$d=\sqrt{\left(y_{2}-y_{1}\right)^{2}+\left(x_{2}-x_{1}\right)^{2}}$

Substituting the coordinates $(3,2)$ and $(x,\frac{3}{4} x-\frac{1}{4})$ in the formula, we have,

$\sqrt{\left(\frac{3 x}{4}-\frac{1}{4}-2\right)^{2}+(x-3)^{2}}=5$

Simplifying, we have,

   $\left(\frac{3 x}{4}-\frac{1}{4}-2\right)^{2}+(x-3)^{2}=25$

$\frac{9x^{2} }{16} -\frac{54x}{16} +\frac{81}{16} +x^{2} -6x+9=25$

Adding the like terms, we have,

$\frac{25x^{2} }{16} -\frac{150x}{16} -\frac{175}{16} =0$

Adding all the terms, we get,

$\frac{25x^{2}-150x-175 }{16} =0$

Multiplying both sides by 16, we get,

$25 x^{2}-150 x-175=0$

Taking out the common term 25 and dividing 25 on both sides, we have,

$x^{2} -6x-7=0$

Factoring, we get,

$(x-7)(x+1)=0$

Thus, $x=-1$ and $x=7$

Substituting $x=-1$ in $y=\left\frac{3}{4}\right x-\frac{1}{4}$ , we get,

$y=\left\frac{3}{4}\ (-1) -\frac{1}{4}$

$y=\left\frac{-3}{4}-\frac{1}{4}$

$y=-1$

Thus, the coordinate is $(-1,-1)$

Also, substituting $x=7$ in $y=\left\frac{3}{4}\right x-\frac{1}{4}$ , we get,

$y=\left\frac{3}{4}\ (7) -\frac{1}{4}$

$y=\left\frac{21}{4}-\frac{1}{4}$

$y=\left\frac{20}{4}$

$y=5$

Thus, the coordinate is $(7,5)$

Hence, the coordinates are $(7,5),(-1,-1)$

Therefore, Option B is the correct answer.

Learn more:

(1) A straight line is passing through the point a(1,2) with slope 5/12 find points on the line which are 13 units away from a

brainly.in/question/5032893

(2) The slope of a straight line passing through A (3,-4) is 5/12 the points on the line that are 26 unit away from A are

brainly.in/question/7237668