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Department of MathematicsMATH1003TUTORIAL 1 : Questions1. Derive the distance formula between two points inR3:P= (x1, y1, z1),andQ= (x2, y2, z2)2. Find the slope of each line.(i) Through (1,5) and (1,3)(ii) A line perpendicular to 5x=y-23. Find an equation for each line(i) Vertical line through (-8,1)(ii)x-intercept 2 andy-intercept 4(iii) Through (2,-3), parallel to 2y-4 =x.4. Use slopes to show that the square with vertices at (-2,5), (4,5), (4,-1) and (-2,-1)has diagonals that are perpendicular.5. Use slopes and the distance formula to show that the quadrilateral whose vertices are(0,0), (1,3), (4,2) and, (3,-1) is a square.6. Given two points A and B on thexy-plane whose coordinates are (0,4) and (5,4)respectively, find all possible pointsCon the liney= 2 such that these three pointsform a right triangle.7. Find the domain of each function.(a)f(x) =2√15x2+x-2(b)f(x) =rx+ 1x-18. Find the intercepts and symmetries of the following zodiacal sign Capricorn given bythe equationx2(x2+y2)-2(y-x2-y2)2= 0.9. Graph the functiony=|x2-4|.10. A farmer with 4000 meters of fencing wants to enclose a rectangular plot that borders