Mathematics
In what ratio does the point M(p, -1) divide the line segment joining the points A(1, -3) and B(6, 2) ? Hence, find the value of p.
Related Questions
Points A and B have the coordinates (-2, 4) and (-4, 1) respectively. Find :
(i) the co-ordinates of A', the image of A in the line x = 0.
(ii) the coordinates of B', the image of B in the y-axis.
(iii) the coordinates of A", the image of A in the line BB'.
Hence, write the angle between the lines A'A" and BB'. Assign a special name to the figure B'A'BA".
Triangle OA1B1 is the reflection of triangle OAB in origin, where A1 (4, -5) is the image of A and B1 (-7, 0) is the image of B.
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(i) Write down the co-ordinates of A and B and draw a diagram to represent this information.
(ii) Give a special name to the quadrilateral ABA1B1. Give reason.
(iii) Find the co-ordinates of A2, the image of A under reflection in x-axis followed by reflection in y-axis.
(iv) Find the co-ordinates of B2, the image of B under reflection in y-axis followed by reflection in origin.
A(-4, 4), B(x, -1) and C(6, y) are the vertices of △ABC. If the centroid of this triangle ABC is at the origin, find the values of x and y.
A(2, 5), B(-1, 2) and C(5, 8) are the vertices of △ABC. P and Q are points on AB and AC respectively such that AP : PB = AQ : QC = 1 : 2.
(a) Find the coordinates of points P and Q.
(b) Show that BC = 3 × PQ.
