Advertisements
Advertisements
Question
Find the relation between x and y if, the points A(x, y), B(-5, 7) and C(-4, 5) are collinear.
Solution
Given, the pointsA(x,y), B(-5,7) and C(-4,5) are collinear.
So, the area formed by these vertices is 0.
1/2[x(7-5)+(-5)(5-y)+(-4)(y-7)= 0
1/2[2x-25+5y-4y+28]= 0
1/2[2x+y+3]= 0
2x+y+3 = 0
y = -2x- 3
APPEARS IN
RELATED QUESTIONS
Find the area of a triangle whose vertices are A(3, 2), B (11, 8) and C(8, 12).
The vertices of a ΔABC are A (4, 6), B (1, 5) and C (7, 2). A line is drawn to intersect sides AB and AC at D and E respectively, such that `(AD)/(AB) = (AE)/(AC) = 1/4`Calculate the area of the ΔADE and compare it with the area of ΔABC. (Recall Converse of basic proportionality theorem and Theorem 6.6 related to ratio of areas of two similar triangles)
The area of a triangle is 5 sq units. Two of its vertices are (2, 1) and (3, –2). If the third vertex is (`7/2`, y). Find the value of y
Show that the following sets of points are collinear.
(1, −1), (2, 1) and (4, 5)
Prove that the points (a, 0), (0, b) and (1, 1) are collinear if `1/a+1/b=1`
For what value of x are the points A(-3, 12), B(7, 6) and C(x, 9) collinear.
If the area of triangle ABC formed by A(x, y), B(1, 2) and C(2, 1) is 6 square units, then prove that x + y = 15 ?
Find the value of p for which the points (−5, 1), (1, p) and (4, −2) are collinear.
If the points (a1, b1), (a2, b2) and(a1 + a2, b1 + b2) are collinear, then ____________.
Area of a triangle PQR right-angled at Q is 60 cm2 in the figure. If the smallest side is 8 cm long, find the length of the other two sides.
