Point A divides segment BC in the ratio 1 : 3. The co-ordinates of B are (4, -4) and that of C are (0, 6). What are the co-ordinates of point A?
(3, -1.5)
By the section formula, point A dividing BC internally in ratio \(m:n = 1:3\) has coordinates:
\[A=\left(\frac{mx_2+nx_1}{m+n},\frac{my_2+ny_1}{m+n}\right)\]
With \(B(4,-4)\), \(C(0,6)\):
\[A=\left(\frac{1(0)+3(4)}{4},\frac{1(6)+3(-4)}{4}\right)=\left(\frac{12}{4},\frac{-6}{4}\right)=(3,-1.5)\]
Therefore \(A=\mathbf{(3,-1.5)}\).
Similar Questions
If angles of a triangle are in the ration of 2 : 3 : 4, then the measure of the smallest angle is:
The distance between the points (4, 8) and (k, -4) is 13. What is the value of k?
What is the reflection of the point (-0.5, 6) in the x-axis?
In the triangle, if AB = AC and ∠ABC = 72°, then ∠BAC is:
In a ΔABC, the bisectors of ∠B and ∠C meet at point O, inside the triangle. If ∠BOC = 122°, then the measure of ∠A is:
In the given figure ΔABC, if θ = 80°, the measure of each of the other two angles will be:
The angles of a triangle are (8x - 15)°,(6x - 11)° and ( 4x – 10)°. What is the value of x ?
What is the equation of a line having a slope -1/3 and y-intercept equal to 6?
In the given figure, ABC is a triangle. The bisectors of internal DB and external DC interest at D. If ∠BDC = 48°, then what is the value (in degrees) of ∠A?
In ΔPQR, QT ⊥ PR and S is a point on QR such that ∠PSQ = p°. If ∠TQR = 46° and ∠SPR = 32°, then the value of p is∶
Important Questions from Lines and Angles
Two parallel lines are intersected by a transversal, the corresponding angles are:
If l, m, n are lines such that, l is parallel to n and m is parallel to n, then, ______
There are three points P, Q and R on a straight line such that PQ : QR = 3 : 5. If n is the number of possible values of PQ : PR, then what is n equal to ?
Two cars start from a point at the same time and travel on two different roads at right angles to each other. Their speed is 18 km/h and 72 km/h respectively. What will be the distance between them after 6 seconds?
If angles of a triangle are in the ration of 2 : 3 : 4, then the measure of the smallest angle is:
