Advertisements
Advertisements
प्रश्न
If the point \[C \left( - 1, 2 \right)\] divides internally the line segment joining the points A (2, 5) and B( x, y ) in the ratio 3 : 4 , find the value of x2 + y2 .
Advertisements
उत्तर
It is given that the point C(–1, 2) divides the line segment joining the points A(2, 5) and B(x, y) in the ratio 3 : 4 internally.
Using the section formula, we get
\[\left( - 1, 2 \right) = \left( \frac{3 \times x + 4 \times 2}{3 + 4}, \frac{3 \times y + 4 \times 5}{3 + 4} \right)\]
\[ \Rightarrow \left( - 1, 2 \right) = \left( \frac{3x + 8}{7}, \frac{3y + 20}{7} \right)\]
\[ \Rightarrow \frac{3x + 8}{7} = - 1\text{ and } \frac{3y + 20}{7} = 2\]
⇒ 3x + 8 = –7 and 3y + 20 = 14
⇒ 3x = –15 and 3y = –6
⇒ x = –5 and y = –2
∴ x2 + y2 = 25 + 4 = 29
Hence, the value of x2 + y2 is 29.
APPEARS IN
संबंधित प्रश्न
If the points A(k + 1, 2k), B(3k, 2k + 3) and C(5k − 1, 5k) are collinear, then find the value of k
Find the third vertex of a triangle, if two of its vertices are at (−3, 1) and (0, −2) and the centroid is at the origin.
Name the quadrilateral formed, if any, by the following points, and given reasons for your answers:
A(-3, 5) B(3, 1), C (0, 3), D(-1, -4)
Prove that the points (3, 0), (4, 5), (-1, 4) and (-2, -1), taken in order, form a rhombus.
Also, find its area.
The line segment joining the points A(3,−4) and B(1,2) is trisected at the points P(p,−2) and Q `(5/3,q)`. Find the values of p and q.
Find the area of quadrilateral ABCD whose vertices are A(-5, 7), B(-4, -5) C(-1,-6) and D(4,5)
Find the area of the triangle formed by joining the midpoints of the sides of the triangle whose vertices are A(2,1) B(4,3) and C(2,5)
Show that ΔABC, where A(–2, 0), B(2, 0), C(0, 2) and ΔPQR where P(–4, 0), Q(4, 0), R(0, 2) are similar triangles.
If the points P, Q(x, 7), R, S(6, y) in this order divide the line segment joining A(2, p) and B(7, 10) in 5 equal parts, find x, y and p.
If the point P (m, 3) lies on the line segment joining the points \[A\left( - \frac{2}{5}, 6 \right)\] and B (2, 8), find the value of m.
If three points (x1, y1) (x2, y2), (x3, y3) lie on the same line, prove that \[\frac{y_2 - y_3}{x_2 x_3} + \frac{y_3 - y_1}{x_3 x_1} + \frac{y_1 - y_2}{x_1 x_2} = 0\]
If P (2, p) is the mid-point of the line segment joining the points A (6, −5) and B (−2, 11). find the value of p.
The distance between the points (cos θ, 0) and (sin θ − cos θ) is
If three points (0, 0), \[\left( 3, \sqrt{3} \right)\] and (3, λ) form an equilateral triangle, then λ =
The distance of the point (4, 7) from the y-axis is
Any point on the line y = x is of the form ______.
In which quadrant does the point (-4, -3) lie?
In the above figure, seg PA, seg QB and RC are perpendicular to seg AC. From the information given in the figure, prove that: `1/x + 1/y = 1/z`
Statement A (Assertion): If the coordinates of the mid-points of the sides AB and AC of ∆ABC are D(3, 5) and E(–3, –3) respectively, then BC = 20 units.
Statement R (Reason): The line joining the mid-points of two sides of a triangle is parallel to the third side and equal to half of it.
The coordinates of the point where the line 2y = 4x + 5 crosses x-axis is ______.
