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
Construct a triangle ABC in which AB = 5 cm, BC = 6 cm and ∠ABC = 60˚. Now construct another triangle whose sides are 5/7 times the corresponding sides of ΔABC.
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.
Construct a triangle with sides 5 cm, 6 cm and 7 cm and then another triangle whose sides are `7/5` of the corresponding sides of the first triangle. 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.
Construct an isosceles triangle with base 8 cm and altitude 4 cm. Construct another triangle whose sides are `2/3` times the corresponding sides of the isosceles triangle.
Divide a line segment of length 14 cm internally in the ratio 2 : 5. Also, justify your construction.
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°.
Draw a ΔABC in which BC = 6 cm, AB = 4 cm and AC = 5 cm. Draw a triangle similar to ΔABC with its sides equal to (3/4)th of the corresponding sides of ΔABC.
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.
Draw a line segment of length 7.6 cm and divide it in the ratio 5:8. Measure the two parts.
Construct a right triangle in which the sides, (other than the hypotenuse) are of length 6 cm and 8 cm. Then construct another triangle, whose sides are `3/5` times the corresponding sides of the given triangle.
∆ABC ~ ∆LBN. In ∆ABC, AB = 5.1 cm, ∠B = 40°, BC = 4.8 cm, \[\frac{AC}{LN} = \frac{4}{7}\]. Construct ∆ABC and ∆LBN.
Construct ∆PYQ such that, PY = 6.3 cm, YQ = 7.2 cm, PQ = 5.8 cm. If \[\frac{YZ}{YQ} = \frac{6}{5},\] then construct ∆XYZ similar to ∆PYQ.
Find the co-ordinates of the points of trisection of the line segment AB with A(2, 7) and B(–4, –8).
Given A(4, –3), B(8, 5). Find the coordinates of the point that divides segment AB in the ratio 3 : 1.
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`.
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 \[\frac{3}{5}\] times the corresponding sides of the given triangle.
Δ AMT ∼ ΔAHE. In Δ AMT, MA = 6.3 cm, ∠MAT = 120°, AT = 4.9 cm, `(MA)/(HA) = 7/5`. construct Δ AHE.
Find the co-ordinates of the centroid of the Δ PQR, whose vertices are P(3, –5), Q(4, 3) and R(11, –4)
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.
______ number of tangents can be drawn to a circle from the point on the circle.
∆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 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 ______.
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 ______.
A triangle ABC is such that BC = 6cm, AB = 4cm and AC = 5cm. For the triangle similar to this triangle with its sides equal to `3/4`th of the corresponding sides of ΔABC, correct figure is?
For ∆ABC in which BC = 7.5cm, ∠B =45° and AB - AC = 4, select the correct figure.
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.
When a line segment is divided in the ratio 2 : 3, how many parts is it divided into?
If the perpendicular distance between AP is given, which vertices of the similar triangle would you find first?
Match the following based on the construction of similar triangles, if scale factor `(m/n)` is.
| Column I | Column II | ||
| i | >1 | a) | The similar triangle is smaller than the original triangle. |
| ii | <1 | b) | The two triangles are congruent triangles. |
| iii | =1 | c) | The similar triangle is larger than the original 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.
The basic principle used in dividing a line segment is ______.
Draw a line segment of length 7.5 cm and divide it in the ratio 1:3.
Draw a line segment of length 7 cm and divide it in the ratio 5 : 3.
