Mathematics
Sketch and describe the locus of the vertices of all triangles with a given base and a given altitude.
Locus
4 Likes
Answer
Steps of construction :
Draw a line segment BC.
Draw XY, perpendicular bisector of BC intersecting BC at D and cut off DA, such that DA = altitude.
Draw a line segment EF parallel to BC at a distance = altitude and passing through A.
Hence, the line EF is the locus of the vertices of all triangles with a given base and a given altitude.
Answered By
2 Likes
Related Questions
In the given figure, obtain all the points equidistant from lines m and n; and 2.5 cm from O.
A straight line AB is 8 cm long. Draw and describe the locus of a point which is :
(i) always 4 cm from the line AB.
(ii) equidistant from A and B.
Mark the two points X and Y, which are 4 cm from AB and equidistant from A and B. Describe the figure AXBY.
Describe :
(i) The locus of points at distances less than 3 cm from a given point.
(ii) The locus of points at distances greater than 4 cm from a given point.
(iii) The locus of points at distances less than or equal to 2.5 cm from a given point.
(iv) The locus of points at distances greater than or equal to 35 mm from a given point.
(v) The locus of the center of a given circle which rolls around the outside of a second circle and is always touching it.
(vi) The locus of the centers of all circles that are tangent to both the arms of a given angle.
(vii) The locus of the mid-points of all chords parallel to a given chord of a circle.
(viii) The locus of points within a circle that are equidistant from the end points of a given chord.
Draw a triangle ABC in which AB = 6 cm, BC = 4.5 cm and AC = 5 cm. Draw and label :
(i) the locus of the centers of all circles which touch AB and AC,
(ii) the locus of the centers of all the circles of radius 2 cm which touch AB.
Hence, construct the circle of radius 2 cm which touches AB and AC.