Advertisements
Advertisements
प्रश्न
P(3, 4), Q(7, –2) and R(–2, –1) are the vertices of triangle PQR. Write down the equation of the median of the triangle through R.
उत्तर
Let median through R be RX.
We know that, the median, RX through R will bisect the line PQ.
By Mid-point formula,
Mid-point = `((x_1 + x_2)/2, (y_1 + y_2)/2)`
The co-ordinates of point X are
`((3 + 7)/2, (4 +(-2))/2)`
= `(10/2, 2/2)`
= (5, 1)
By formula,
Slope = `(y_2 - y_1)/(x_2 - x_1)`
Substituting values we get,
Slope of RX = `(1 - (-1))/(5 - (-2)) = 2/7`
Then, the required equation of the median RX is given by
`=>` y − y1 = m(x − x1)
`=> y - (-1) = 2/7[x - (-2)]`
`=> y + 1 = 2/7(x + 2)`
`=>` 7(y + 1) = 2(x + 2)
`=>` 7y + 7 = 2x + 4
`=>` 7y = 2x – 3
Hence, equation of the median through R is 7y = 2x – 3.
APPEARS IN
संबंधित प्रश्न
In the given figure ABCD is a rectangle. It consists of a circle and two semi-circles each of
which are of radius 5 cm. Find the area of the shaded region. Give your answer correct to
three significant figures
Three vertices of parallelogram ABCD taken in order are A(3, 6), B(5, 10) and C(3, 2)
1) the coordinate of the fourth vertex D
2) length of diagonal BD
3) equation of the side AD of the parallelogram ABCD
Using a graph paper, plot the points A(6, 4) and B(0, 4).
- Reflect A and B in the origin to get the images A' and B'.
- Write the co-ordinates of A' and B'.
- State the geometrical name for the figure ABA'B'.
- Find its perimeter.
Show that A(3, 2), B(6, −2) and C(2, −5) can be the vertices of a square.
- Find the co-ordinates of its fourth vertex D, if ABCD is a square.
- Without using the co-ordinates of vertex D, find the equation of side AD of the square and also the equation of diagonal BD.
O(0, 0), A(3, 5) and B(−5, −3) are the vertices of triangle OAB. Find the equation of median of triangle OAB through vertex O.
O(0, 0), A(3, 5) and B(−5, −3) are the vertices of triangle OAB. Find the equation of altitude of triangle OAB through vertex B.
Point A and B have co-ordinates (7, −3) and (1, 9) respectively. Find:
- the slope of AB.
- the equation of perpendicular bisector of the line segment AB.
- the value of ‘p’ of (−2, p) lies on it.
Use a graph sheet for this question.
Take 1 cm = 1 unit along both x and y axis.
(i) Plot the following points:
A(0,5), B(3,0), C(1,0) and D(1,–5)
(ii) Reflect the points B, C and D on the y axis and name them as B',C'andD' respectively.
(iii) Write down the coordinates of B',C 'and D'
(iv) Join the point A, B, C, D, D ', C ', B', A in order and give a name to the closed figure ABCDD'C'B
A line is of length 10 units and one end is at the point (2, – 3). If the abscissa of the other end be 10, prove that its ordinate must be 3 or – 9.
Use a graph sheet for this question, take 2 cm = 1 unit along both x and y-axis:
- Plot the points A (3, 2) and B (5, 0). Reflect point A on the y-axis to A΄. Write co-ordinates of A΄.
- Reflect point B on the line AA΄ to B΄. Write the co-ordinates of B΄.
- Name the closed figure A’B’AB.
