91Ó°ÊÓ

The real numbers \(a, b, c,\) and \(d\) are positive. Consider the triangle with vertices at \(A(0,0), B(a, 0)\) and \(C(a, b) .\) Explain why \(\triangle A B C\) is a right triangle. CAN'T COPY THE GRAPH

In Exercises 1 to \(8,\) draw the graph of each equation. Name any intencepts. $$2 x+6=0$$

For the line \(\ell:(x, y, z)=(5,-3,2)+n(1,2,-2),\) find a) a point of the line. b) a direction vector for the line.

In Exercises 1 to \(8,\) draw the graph of each equation. Name any intencepts. $$3 y-9=0$$

Find an expression for the distance between \((a, b)\) and \((a, c)\) if \(b>c\)

The real numbers \(a, b, c,\) and \(d\) are positive. Consider the triangle with vertices at \(R(-a, 0), S(a, 0)\)and \(T(0, b) .\) Explain why \(\triangle R S T\) is an isosceles triangle. CAN'T COPY THE GRAPH

In Exercises 1 to \(8,\) draw the graph of each equation. Name any intencepts. $$\frac{1}{2} x+y=3$$

The real numbers \(a, b, c,\) and \(d\) are positive. Consider the quadrilateral with vertices at \(M(0,0)\) \(N(a, 0), P(a+b, c),\) and \(Q(b, c) .\) Explain why \(M N P Q\) is a parallelogram. CAN'T COPY THE GRAPH

Line \(m\) is expressed in point form \((x, y, z)=(2+3 n, 4-5 n, 5+2 n) .\) Find a) a point of the line. b) a direction vector for the line.

Find the distance between each pair of points: a) \((0,-3)\) and \((4,0)\) b) \((-2,5)\) and \((4,-3)\) c) \((3,2)\) and \((5,-2)\) d) \(\quad(a, 0)\) and \((0, b)\)