42. Area of A ABC is 5 square unit. It has two vertices A(2, 1) and B(3,-2). Its third vertice C is lying on line y - x+3 = 0. Find coordinates of point C.
The area of a triangle is 5 square units, two of its vertices are (2, 1) and (3, -2). The third vertex lies on y = x+ 3. What will be the third vertex ?
Answers & Comments
Step-by-step explanation:
search-icon-image
Question
Bookmark
The area of a triangle is 5 square units, two of its vertices are (2, 1) and (3, -2). The third vertex lies on y = x+ 3. What will be the third vertex ?
Medium
Solution
verified
Verified by Toppr
Correct option is B)
Area o a triangle = 5sq.unit
Two vertices of △le,A(2,1),B(3,−2),C(x,y)
Third vertex lies on the line y=x+3→(1)
Area
2
1
[x
1
(y
2
−y
3
)+x
2
(y
3
−y
1
)+x
3
(y
1
−y
2
)]=5
⇒[2[−2−y]+3[y−1]+x(1+2)]=10
−4−2y+3y−3+3x=10
⇒y+3x=17→(2)
Solving (1) and (2)
∴4x=14
y+3x=17y−x=3
⇒x=
2
7
y=
2
7
+3=
2
13
∴(x,y)=(
2
7
,
2
13
)
Answer:
a=0, b=-3
hope this help you