Advertisements
Advertisements
प्रश्न
The line segment joining A (2, 3) and B (6, – 5) is intersected by the X axis at the point K. Write the ordinate of the point K. Hence find the ratio in which K divides AB.
उत्तर
A (2, 3) and B (6,- 5)
Intersected at X axis at K.
∴ y = 0 or ordinate = 0
K (x, 0)
Let required ratio be a: 1
∴ Ordinate of K = 0
0 = `(a xx -5 + 1 xx 3)/(a + 1)`
0 = -5a + 3
5a = 3, a = `(3)/(5)`
∴ K divides AB in ratio of 3 : 5.
APPEARS IN
संबंधित प्रश्न
Calculate the ratio in which the line joining A(-4,2) and B(3,6) is divided by point p(x,3). Also, find x
If the abscissa of a point P is 2, find the ratio in which this point divides the line segment joining the point (−4, 3) and (6, 3). Also, find the co-ordinates of point P.
The line joining the points (2, 1) and (5, –8) is trisected at the point P and Q. If point P lies on the line 2x – y + k = 0, find the value of k. Also, find the co-ordinates of point Q.
Find the image of the point A(5, –3) under reflection in the point P(–1, 3).
A(–4, 2), B(0, 2) and C(–2, –4) are vertices of a triangle ABC. P, Q and R are mid-points of sides BC, CA and AB respectively. Show that the centroid of ΔPQR is the same as the centroid of ΔABC.
Prove that the points A(-5, 4), B(-1, -2) and C(S, 2) are the vertices of an isosceles right-angled triangle. Find the coordinates of D so that ABCD is a square.
Show that the points A(1, 3), B(2, 6), C(5, 7) and D(4, 4) are the vertices of a rhombus.
= `a(1/t^2 + 1) = (a(t^2 + 1))/t^2`
Now `(1)/"SP" + (1)/"SQ" = (1)/(a(t^2 + 1)) + (1 xx t^2)/(a(t^2 + 1)`
= `((1 + t^2))/(a(t^2 + 1)`
`(1)/"SP" + (1)/"SQ" = (1)/a`.
Determine the ratio in which the line 3x + y – 9 = 0 divides the line joining (1, 3) and (2, 7).
Determine the centre of the circle on which the points (1, 7), (7 – 1), and (8, 6) lie. What is the radius of the circle?
From the adjacent figure:
(i) Write the coordinates of the points A, B, and
(ii) Write the slope of the line AB.
(iii) Line through C, drawn parallel to AB, intersects Y-axis at D. Calculate the co-ordinates of D.
