Mathematics
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.
Related Questions
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.
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.
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.
Show that the points (a, b), (a + 3, b + 4), (a - 1, b + 7) and (a - 4, b + 3) are the vertices of a parallelogram.