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in the triangle ABC having vertices at A(-2,5), B(6,1) and C(-2,-3), find the length of the median from vertex B to side AC.
x=5^1/4 5^-1/4 y=5^1/4 - 5^-1/4 prove that 5(x² y²)²=144?
a. The points 𝐴,𝐵 and 𝐶 have co-ordinates (−1,2),(1,1) and (2,3) respectively. Sketch the triangle 𝐴𝐵𝐶 .By calculating the lengths of the sides of this triangle, determine if it is scalene, isosceles, or equilateral.
b. Find the distance 𝑀𝐵, where 𝑀 is the midpoint of 𝐴𝐶, and hence find the area of the triangle 𝐴𝐵𝐶.
a. The points 𝐴,𝐵 and 𝐶 have co-ordinates (−1,2),(1,1) and (2,3) respectively. Sketch the triangle 𝐴𝐵𝐶. By calculating the lengths of the sides of this triangle, determine if it is scalene, isosceles, or equilateral.
The line joining the point 𝐴 (4,6) 𝑡𝑜 𝐵 (𝑏,−3) has a gradient of 3. Find the value of 𝑏.
𝑃 and 𝑄 are the points (3,1) and (−2,−9) respectively. Calculate:
a. The distance 𝑃𝑄
b. The midpoint of the line joining 𝑃 to 𝑄
c. The gradient of the line 𝑃𝑄
d. The gradient of a line perpendicular to 𝑃𝑄
Find the equation of tangent plane to the conicoid 𝑥2 + 3𝑦2 = 4𝑧 at (2, −4, 13). Represent the tangent plane geometrically.
Identify and trace the conicoid 𝑦2 + 3𝑧2 = 𝑥. Describe its sections by the planes 𝑦 = 0 and 𝑧 = 0.
Find the projection of the line segment joining the points (1, −1, 6) and (4, 3, 2) on the line (𝑥−4)/3 = −𝑦 = 𝑧/5 .
Find the transformation of the equation 12𝑥2 − 2𝑦2 + 𝑧2 = 2𝑥𝑦 if the origin is kept fixed and the axes are rotated in such a way that the direction ratios of the new axes are 1, −3, 0; 3, 1, 0; 0, 0, 1
