Question

If the points A(1, 2), B(k+1, 2) and C(6, 7) are the vertices of a triangle having B = 90°, find the value of K

The one who answers this question the fastest will definitely be marked as the brainliest;)​

Answer 1

Answer:

k=5

Step-by-step explanation:

Let the points A and B lie on a line. We can form an equation of the line by taking in their coordinates.

$y - y_{1} = m(x - x_{1} )$

Now let us find out the slope of the line. For doing so, we can use the formula.

$m = \frac{y_{2} - y_{1} }{x_{2} -x_{1} } \\ m = \frac{2 - 2}{1 - k - 1} \\ m = 0$

So the equation of the line connecting the points A and B turn out to be,

$y - 2 = 0(x - 1)$

We can make out the that the line is parallel to the x axis.

Now we are given that B=90°. That means the line joining the points B and C will be perpendicular to the lines joining the points A and B. From here, we can make out that the line joining B and C will have an infinite slope or will be parallel to the y axis.

For lines parallel to the y axis we have,

$m(y - y_{1}) = x - x_{1} \\ m = 0 \\ 0(y - y_{1}) = x - x_{1}$

Hence, we know that there will be no change in the x-coordinate along the line joining B and C.

We can use this fact to our advantage since

$x_{1} = x_{2}$

And so we can equate the x-coordinates of points B and C

$k + 1 = 6 \\ k = 5$