Mathematics
Find the equation of the straight line perpendicular to the line x + 2y = 4, which cuts an intercept of 2 units from the positive y-axis. Hence, find the intersection point of the two lines.
Related Questions
(a) Point P(2, -3) on reflection becomes P'(2, 3). Name the line of reflection (say L1).
(b) Point P' is reflected to P'' along the line (𝐿2), which is perpendicular to the line 𝐿1 and passes through the point, which is invariant along both axes. Write the coordinates of P''.
(c) Name and write the coordinates of the point of intersection of the lines 𝐿1 and 𝐿2.
(d) Point P is reflected to P''' on reflection through the point named in the answer of part I of this question. Write the coordinates of P'''. Comment on the location of the points P'' and P'''.
In the given figure, if the line segment AB is intercepted by the y-axis and x-axis at C and D, respectively, such that AC : AD = 1 : 4 and D is the midpoint of CB. Find the coordinates of D, C and B.
While preparing a PowerPoint presentation, ∆ ABC is enlarged along the side BC to ∆ AB'C', as shown in the diagram, such that BC ∶ B'C' is 3 ∶ 5. Find :
(a) AB ∶ BB'
(b) length AB, if BB' = 4 cm.
(c) Is ∆ ABC ~ ∆ AB'C' ? Justify your answer.
(d) ar (∆ ABC) : ar (quad. BB'C'C).
The approximate volume of a human eye is 6.5 cm3. The volume of a laboratory model (excluding base and stand) of the human eye is 1404 cm3.
(a) State whether the scale factor k is less than, equals to or greater than 1.
(b) Calculate the:
(i) value of k
(ii) diameter of the human eye if the radius of the model is 7.2 cm.
(iii) the external surface area of the human eye if the surface area of the model is 651.6 cm2.