Question 1

Find the distance between Y and the midpoint of segment XZ given X[-1,4], Y[-2,-3], Z[5,2]. Please show me how to solve this step by step.

Question 2

well, to find what that middle point is on XZ

$\bf \textit{middle point of 2 points }\\ \quad \\ \begin{array}{lclclll} &x_1&y_1&x_2&y_2\\ % (a,b) &X({{ -1}}\quad ,&{{ 4}})\quad % (c,d) &Z({{ 5}}\quad ,&{{ 2}}) \end{array}\qquad % coordinates of midpoint \left(\cfrac{{{ x_2}} + {{ x_1}}}{2}\quad ,\quad \cfrac{{{ y_2}} + {{ y_1}}}{2} \right)$

once you found that, then use it in the distance equation

$\bf \textit{distance between 2 points}\\ \quad \\ \begin{array}{lcllll} &x_1&y_1&x_2&y_2\\ % (a,b) &Y({{ -2}}\quad ,&{{ -3}})\quad % (c,d) &({{ \square }}\quad ,&{{ \square }}) \end{array}\qquad % distance value d = \sqrt{({{ x_2}}-{{ x_1}})^2 + ({{ y_2}}-{{ y_1}})^2}$

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