Advertisements
Advertisements
Question
If A(–14, –10), B(6, –2) is given, find the coordinates of the points which divide segment AB into four equal parts.
Advertisements
Solution
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).
RELATED QUESTIONS
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.
ΔRST ~ ΔUAY, In ΔRST, RS = 6 cm, ∠S = 50°, ST = 7.5 cm. The corresponding sides of ΔRST and ΔUAY are in the ratio 5 : 4. Construct ΔUAY.
Find the ratio in which the line segment joining the points A(3,- 3) and B(- 2, 7) is divided by x-axis. Also find the coordinates of the point of division.
Construct a triangle ABC in which BC = 6 cm, AB = 5 cm and ∠ABC = 60°. Then construct another triangle whose sides are`3/4` times the corresponding sides of ΔABC.
Draw a triangle ABC with BC = 7 cm, ∠B = 45° and ∠A = 105°. Then construct a triangle whose sides are`4/5` times the corresponding sides of ΔABC.
Draw a triangle ABC with side BC = 7 cm, ∠B = 45°, ∠A = 105°. Then, construct a triangle whose sides are `4/3 `times the corresponding side of ΔABC. Give the justification of the construction.
Draw a right triangle in which the sides (other than the hypotenuse) are of lengths 4 cm and 3 cm. Now construct another triangle whose sides are `3/5` times the corresponding sides of the given triangle.
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°.
Construct a triangle similar to a given ΔABC such that each of its sides is (2/3)rd of the corresponding sides of ΔABC. It is given that BC = 6 cm, ∠B = 50° and ∠C = 60°.
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.
Draw a right triangle in which sides (other than the hypotenuse) are of lengths 8 cm and 6 cm. Then construct another triangle whose sides are 3/4 times the corresponding sides of the first triangle.
∆PQR ~ ∆LTR. In ∆PQR, PQ = 4.2 cm, QR = 5.4 cm, PR = 4.8 cm. Construct ∆PQR and ∆LTR, such that `"PQ"/"LT" = 3/4`.
∆AMT ~ ∆AHE. In ∆AMT, AM = 6.3 cm, ∠TAM = 50°, AT = 5.6 cm. `"AM"/"AH" = 7/5`. Construct ∆AHE.
∆ABC ~ ∆LBN. In ∆ABC, AB = 5.1 cm, ∠B = 40°, BC = 4.8 cm, \[\frac{AC}{LN} = \frac{4}{7}\]. Construct ∆ABC and ∆LBN.
Given A(4, –3), B(8, 5). Find the coordinates of the point that divides segment AB in the ratio 3 : 1.
Find the co-ordinates of the centroid of the Δ PQR, whose vertices are P(3, –5), Q(4, 3) and R(11, –4)
Choose the correct alternative:
ΔPQR ~ ΔABC, `"PR"/"AC" = 5/7`, then
Choose the correct alternative:
∆ABC ∼ ∆AQR. `"AB"/"AQ" = 7/5`, then which of the following option is true?
Construct an equilateral ∆ABC with side 5 cm. ∆ABC ~ ∆LMN, ratio the corresponding sides of triangle is 6 : 7, then construct ΔLMN and ΔABC
To divide a line segment AB in the ratio p : q (p, q are positive integers), draw a ray AX so that ∠BAX is an acute angle and then mark points on ray AX at equal distances such that the minimum number of these points is ______.
To divide a line segment AB in the ratio 4 : 7, a ray AX is drawn first such that ∠BAX is an acute angle and then points A1, A2, A3, .... are located at equal distances on the ray AX and the point B is joined to ______.
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′.
The image of construction of A’C’B a similar triangle of ΔACB is given below. Then choose the correct option.
The point W divides the line XY in the ratio m : n. Then, the ratio of lengths of the line segments XY : WX is ______.
By geometrical construction, it is possible to divide a line segment in the ratio `sqrt(3) : 1/sqrt(3)`.
Draw a line segment of length 7 cm. Find a point P on it which divides it in the ratio 3:5.
Draw a right triangle ABC in which BC = 12 cm, AB = 5 cm and ∠B = 90°. Construct a triangle similar to it and of scale factor `2/3`. Is the new triangle also a right triangle?
Two line segments AB and AC include an angle of 60° where AB = 5 cm and AC = 7 cm. Locate points P and Q on AB and AC, respectively such that AP = `3/4` AB and AQ = `1/4` AC. Join P and Q and measure the length PQ.
Draw an isosceles triangle ABC in which AB = AC = 6 cm and BC = 5 cm. Construct a triangle PQR similar to ∆ABC in which PQ = 8 cm. Also justify the construction.
Draw a triangle ABC in which AB = 4 cm, BC = 6 cm and AC = 9 cm. Construct a triangle similar to ∆ABC with scale factor `3/2`. Justify the construction. Are the two triangles congruent? Note that all the three angles and two sides of the two triangles are equal.
