In Delta ABC,if A(1, 7),B(2, 4),and C(k, 5) a | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(D) Given that $\angle A = 90^{\circ}$,the sides $AB$ and $AC$ are perpendicular to each other.Therefore,the product of their slopes must be $-1$,i.e.

Vedclass · Accepted Answer

$-5$

Vedclass · Answer

(D) Given that $\angle A = 90^{\circ}$,the sides $AB$ and $AC$ are perpendicular to each other.Therefore,the product of their slopes must be $-1$,i.e.,$m_{AB} 	imes m_{AC} = -1$.The slope of a line passing through $(x_1, y_1)$ and $(x_2, y_2)$ is given by $m = \frac{y_2 - y_1}{x_2 - x_1}$.Slope of $AB$ $(m_{AB})$ = $\frac{4 - 7}{2 - 1} = \frac{-3}{1} = -3$.Slope of $AC$ $(m_{AC})$ = $\frac{5 - 7}{k - 1} = \frac{-2}{k - 1}$.Since $m_{AB} 	imes m_{AC} = -1$,we have $(-3) 	imes \left( \frac{-2}{k - 1} ight) = -1$.$\frac{6}{k - 1} = -1$.$6 = -(k - 1)$.$6 = -k + 1$.$k = 1 - 6 = -5$.

In $\Delta ABC$,if $A(1, 7)$,$B(2, 4)$,and $C(k, 5)$ and $\angle A$ is a right angle,then find the value of $k$.

Similar Questions

Find the area of a triangle having the vertices $A(5, 3)$,$B(4, 5)$,and $C(3, 1)$.

The coordinates of the point which is equidistant from the three vertices of the $\triangle AOB$ as shown in the figure are

State whether the following statement is true or false. Justify your answer.
Points $A(3, 1)$,$B(12, -2)$,and $C(0, 2)$ cannot be the vertices of a triangle.

State whether the following statement is true or false. Justify your answer.
The points $A(-1, 0)$,$B(3, 1)$,$C(2, 2)$,and $D(-2, 1)$ are the vertices of a parallelogram.

Find the circumcentre and the area of the triangle with vertices $(7,9), (10,8)$ and $(12,10)$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module