Advertisements
Advertisements
प्रश्न
If A(–14, –10), B(6, –2) is given, find the coordinates of the points which divide segment AB into four equal parts.
Advertisements
उत्तर
Let the points P, Q, and R divide seg AB into four equal parts.
∴ AP = PQ = QR = RB
Point Q is the mid-point of seg AB.
∴ By mid-point formula,
`"x co-ordinate of Q" = (x_1 + x_2)/2 = (−14 + 6)/2 = (−8)/2 = −4`
`"y co-ordinate of Q" = (y_1 + y_2)/2 = (−10 + (−2))/2 = (−10 −2)/2 = (−12)/2 = − 6`
∴ Co-ordinates of Q are (−4, −6).
Point P is the mid-point of seg AQ.
∴ By mid-point formula,
`"x co-ordinate of P" = (x_1 + x_2)/2 = (−14 + (−4))/2 = (−14 −4)/2 = (−18)/2 = −9`
`"y co-ordinate of P" = (y_1 + y_2)/2 = (−10 + (−6))/2 = (−10 −6)/2 = (−16)/2 = −8`
∴ Co-ordinates of P are (−9, −8).
Point R is the mid-point of seg QB.
∴ By mid-point formula,
`"x co-ordinate of R" = (x_1 + x_2)/2 = (−4 + 6)/2 = 2/2 = 1`
`"y co-ordinate of R" = (y_1 + y_2)/2 = (−6 + (−2))/2 = (−6 −2)/2 = (−8)/2 = −4`
∴ Co-ordinates of R are (1, −4).
∴ The coordinates of the points dividing seg AB into four equal parts are P(−9, −8), Q(−4, −6), and R(1, –4).
संबंधित प्रश्न
Write down the equation of a line whose slope is 3/2 and which passes through point P, where P divides the line segment AB joining A(-2, 6) and B(3, -4) in the ratio 2 : 3.
Construct a Δ ABC in which AB = 6 cm, ∠A = 30° and ∠B = 60°, Construct another ΔAB’C’ similar to ΔABC with base AB’ = 8 cm.
Construct a triangle ABC with BC = 7 cm, ∠B = 60° and AB = 6 cm. Construct another triangle whose sides are `3/4` times the corresponding sides of ∆ABC.
Draw a line segment of length 7.6 cm and divide it in the ratio 5:8. Measure the two parts. Give the justification of the construction.
Construct an isosceles triangle whose base is 8 cm and altitude 4 cm and then another triangle whose side are `1 1/2` times the corresponding sides of the isosceles triangle.
Give the justification of the construction
Draw a right triangle in which the sides (other than hypotenuse) are of lengths 4 cm and 3 cm. the construct another triangle whose sides are `5/3` times the corresponding sides of the given triangle. Give the justification of the construction.
Draw a line segment of length 7 cm and divide it internally in the ratio 2 : 3.
Determine a point which divides a line segment of length 12 cm internally in the ratio 2 : 3 Also, justify your construction.
Divide a line segment of length 9 cm internally in the ratio 4 : 3. Also, give justification of the construction.
Construct a triangle similar to a given ΔABC such that each of its sides is (5/7)th of the corresponding sides of Δ ABC. It is given that AB = 5 cm, BC = 7 cm and ∠ABC = 50°.
Draw a right triangle ABC in which AC = AB = 4.5 cm and ∠A = 90°. Draw a triangle similar to ΔABC with its sides equal to (5/4)th of the corresponding sides of ΔABC.
Construct an isosceles triangle whose base is 8 cm and altitude 4 cm and then another triangle whose sides are 3/2 times the corresponding sides of the isosceles triangle.
Construct a triangle similar to ΔABC in which AB = 4.6 cm, BC = 5.1 cm, ∠A = 60° with scale factor 4 : 5.
Construct a triangle similar to a given ΔXYZ with its sides equal to (3/4)th of the corresponding sides of ΔXYZ. Write the steps of construction.
Construct the circumcircle and incircle of an equilateral ∆XYZ with side 6.5 cm and centre O. Find the ratio of the radii of incircle and circumcircle.
Draw a ∆ABC in which AB = 4 cm, BC = 5 cm and AC = 6 cm. Then construct another triangle whose sides are\[\frac{3}{5}\] of the corresponding sides of ∆ABC ?
∆ABC ~ ∆LBN. In ∆ABC, AB = 5.1 cm, ∠B = 40°, BC = 4.8 cm, \[\frac{AC}{LN} = \frac{4}{7}\]. Construct ∆ABC and ∆LBN.
Find the ratio in which point T(–1, 6)divides the line segment joining the points P(–3, 10) and Q(6, –8).
Draw a line segment AB of length 7 cm. Using ruler and compasses, find a point P on AB such that `(AP)/(AB)=3/5`.
Find the ratio in which the segment joining the points (1, –3) and (4, 5) is divided by the x-axis? Also, find the coordinates of this point on the x-axis.
Points P and Q trisect the line segment joining the points A(−2, 0) and B(0, 8) such that P is near to A. Find the coordinates of points P and Q.
In the figure ΔABC ~ ΔADE then the ratio of their corresponding sides is ______.
∆ABC ∼ ∆AQR. `(AB)/(AQ) = 7/5`, then which of the following option is true?
Draw seg AB of length 9 cm and divide it in the ratio 3 : 2.
∆ABC ~ ∆PBQ. In ∆ABC, AB = 3 cm, ∠B = 90°, BC = 4 cm. Ratio of the corresponding sides of two triangles is 7 : 4. Then construct ∆ABC and ∆PBQ.
ΔAMT ~ ΔAHE. In ΔAMT, AM = 6.3 cm, ∠MAT = 120°, AT = 4.9 cm, `(AM)/(HA) = 7/5`, then construct ΔAMT and ΔAHE.
To construct a triangle similar to a given ΔABC with its sides `8/5` of the corresponding sides of ΔABC draw a ray BX such that ∠CBX is an acute angle and X is on the opposite side of A with respect to BC. Then minimum number of points to be located at equal distances on ray BX is ______.
Draw the line segment AB = 5cm. From the point A draw a line segment AD = 6cm making an angle of 60° with AB. Draw a perpendicular bisector of AD. Select the correct figure.
The ratio of corresponding sides for the pair of triangles whose construction is given as follows: Triangle ABC of dimensions AB = 4cm, BC = 5 cm and ∠B= 60°.A ray BX is drawn from B making an acute angle with AB.5 points B1, B2, B3, B4 and B5 are located on the ray such that BB1 = B1B2 = B2B3 = B3B4 = B4B5.
B4 is joined to A and a line parallel to B4A is drawn through B5 to intersect the extended line AB at A’.
Another line is drawn through A’ parallel to AC, intersecting the extended line BC at C’. Find the ratio of the corresponding sides of ΔABC and ΔA′BC′.
If the perpendicular distance between AP is given, which vertices of the similar triangle would you find first?
If you need to construct a triangle with point P as one of its vertices, which is the angle that you need to construct a side of the triangle?
The point W divides the line XY in the ratio m : n. Then, the ratio of lengths of the line segments XY : WX is ______.
What is the ratio `(AC)/(BC)` for the line segment AB following the construction method below?
Step 1: A ray is extended from A and 30 arcs of equal lengths are cut, cutting the ray at A1, A2,…A30
Step 2: A line is drawn from A30 to B and a line parallel to A30B is drawn, passing through the point A17 and meet AB at C.
To divide a line segment, the ratio of division must be ______.
Draw a triangle ABC in which AB = 5 cm, BC = 6 cm and ∠ABC = 60°. Construct a triangle similar to ∆ABC with scale factor `5/7`. Justify the construction.
Draw a line segment AB of length 10 cm and divide it internally in the ratio of 2:5 Justify the division of line segment AB.
Draw a line segment AB of length 6 cm and mark a point X on it such that AX = `4/5` AB. [Use a scale and compass]
