Question

Help me with question a please ! With full workings !

Answer 1

a)






`\bf QP=√((0.5-0)^2+(0-2)^2)\implies QP=√(0.5^2+2^2) \\\\\\ QP=\sqrt{\left( (1)/(2) \right)^2+4}\implies QP=\sqrt{ (1^2)/(2^2)+4}\implies QP=\sqrt{(1)/(4)+4} \\\\\\ QP=\sqrt{(17)/(4)}\implies QP=\cfrac{√(17)}{√(4)}\implies QP=\cfrac{√(17)}{2}`

b)

since QR=QP, that means that QO is an angle bisector, and thus the segments it makes at the bottom of RO and OP, are also equal, thus RO=OP

thus, since the point P is 0.5 units away from the 0, point R is also 0.5 units away from 0 as well, however, is on the negative side, thus R (-0.5, 0)


c)

what's the equation of a line that passes through the points (-0.5, 0) and (0,2)?





`\bf m=\cfrac{(-2)/(1)}{-(1)/(2)}\implies \cfrac{-2}{1}\cdot \cfrac{2}{-1}\implies 4 \\\\\\ % point-slope intercept y-{{ y_1}}={{ m}}(x-{{ x_1}})\implies y-2=4(x-0)\implies y=4x+2\\ \left. \qquad \right. \uparrow\\ \textit{point-slope form}`