[amp_mcq option1=”\\[\\frac{3}{2}\\]” option2=”\\[\\frac{3}{4}\\]” option3=”\\[\\frac{4}{5}\\]” option4=”\\[\\frac{5}{2}\\]” correct=”option3″]<\/p>\n
The area of a triangle can be calculated using the formula:<\/p>\n
$$A = \\frac{1}{2} \\cdot b \\cdot h$$<\/p>\n
where $b$ is the base of the triangle and $h$ is the height of the triangle.<\/p>\n
In this case, the base of the triangle is the line segment connecting $(1, 0)$ and $(2, 2)$. The length of this line segment can be calculated using the Pythagorean theorem:<\/p>\n
$$|(x_1 – x_2)|^2 + |(y_1 – y_2)|^2 = d^2$$<\/p>\n
where $(x_1, y_1)$ and $(x_2, y_2)$ are the coordinates of the two endpoints of the line segment, and $d$ is the length of the line segment.<\/p>\n
In this case, we have:<\/p>\n
$$|(1 – 2)|^2 + |(0 – 2)|^2 = d^2$$<\/p>\n
$$1^2 + 4^2 = d^2$$<\/p>\n
$$d = \\sqrt{1 + 16} = \\sqrt{17}$$<\/p>\n
The height of the triangle is the perpendicular distance from $(1, 0)$ to the line segment connecting $(2, 2)$ and $(4, 3)$. This can be calculated using the formula:<\/p>\n
$$h = \\sqrt{(x_1 – x_2)^2 + (y_1 – y_2)^2}$$<\/p>\n
In this case, we have:<\/p>\n
$$h = \\sqrt{(1 – 2)^2 + (0 – 2)^2} = \\sqrt{5}$$<\/p>\n
Therefore, the area of the triangle is:<\/p>\n
$$A = \\frac{1}{2} \\cdot \\sqrt{17} \\cdot \\sqrt{5} = \\frac{3}{2}$$<\/p>\n
Therefore, the correct answer is $\\boxed{\\frac{3}{2}}$.<\/p>\n","protected":false},"excerpt":{"rendered":"
[amp_mcq option1=”\\[\\frac{3}{2}\\]” option2=”\\[\\frac{3}{4}\\]” option3=”\\[\\frac{4}{5}\\]” option4=”\\[\\frac{5}{2}\\]” correct=”option3″]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[489],"tags":[],"class_list":["post-20032","post","type-post","status-publish","format-standard","hentry","category-linear-algebra","no-featured-image-padding"],"yoast_head":"\n